# [Algebra](/content/learn/algebra/index.html) › Finding the average
Teacher info ▼
Discover how to find the "average" of numbers
**CCSS.MATH.CONTENT.6.SP.B.5C**
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
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Finding the average
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Rad
Deg
!
(
)
C
⌫
sin-1
sin
√
7
8
9
/
cos-1
cos
ln
4
5
6
×
tan-1
tan
_x_ 2
1
2
3
−
π
_e_
_x y_
0
.
=
+
No hints available
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Video
1x
Rad
Deg
!
(
)
C
⌫
sin-1
sin
√
7
8
9
/
cos-1
cos
ln
4
5
6
×
tan-1
tan
_x_ 2
1
2
3
−
π
_e_
_x y_
0
.
=
+
Stuck?
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Learn about functions, graphs, lines, and polynomials. "Algebra" is the math for describing how different things are related.
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Addition and subtraction
[Number line](/content/learn/algebra/number-line/index.html)
Locating integers and non-integers on the number line
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[Addition](/content/learn/algebra/addition/index.html)
Using the number line to add numbers
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Moving left on the number line
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[Adding negatives](/content/learn/algebra/adding-negatives/index.html)
What happens when you add negative numbers?
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[Subtracting negatives](/content/learn/algebra/subtracting-negatives/index.html)
Turns out it's addition!
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[Absolute value](/content/learn/algebra/absolute-value/index.html)
The "size" of a number, or how far it is from zero
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[Number line distance](/content/learn/algebra/distance-1d/index.html)
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Multiplication and division
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Multiplying positive numbers, in any order
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Dividing positive numbers, and ways to think about it
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[Dividing by 0](/content/learn/algebra/divide-by-zero/index.html)
An operation you just can't perform...
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[Order of operations](/content/learn/algebra/pmdas/index.html)
Is there more than one way to evaluate an expression?
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[Distributive law](/content/learn/algebra/distributive-law/index.html)
Getting rid of parentheses when you add and multiply
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[Dividing negatives](/content/learn/algebra/dividing-negatives/index.html)
What happens when you divide negative numbers?
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[Distributing negatives](/content/learn/algebra/distribute-negative/index.html)
Distributing a negative flips the signs
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[\[Brackets\] and {braces}](/content/learn/algebra/brackets/index.html)
What to do when you have too many parentheses!
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[Finding the average](/content/learn/algebra/average/index.html)
Discover how to find the "average" of numbers
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Factoring
[Factors](/content/learn/algebra/factors/index.html)
Dividing by a factor always gives you a whole number
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[Prime numbers](/content/learn/algebra/primes/index.html)
Their only factors are 1 and themselves
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[Factoring out](/content/learn/algebra/factor-out/index.html)
Pulling out common factors using the distributive law
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[Factoring out negatives](/content/learn/algebra/factor-out-negative/index.html)
Flip the signs when you factor out negative numbers
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[Greatest common factor](/content/learn/algebra/greatest-common-factor/index.html)
The biggest factor that numbers have in common
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[Relatively prime](/content/learn/algebra/relatively-prime/index.html)
When two numbers have no common factors
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[Euclid's algorithm](/content/learn/algebra/euclids-algorithm/index.html)
A 2000-year-old way to calculate the GCF
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[Multiples](/content/learn/algebra/multiples/index.html)
What you get when you multiply numbers by integers
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[Least common multiple](/content/learn/algebra/least-common-multiple/index.html)
The smallest multiple numbers have in common
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Fractions
[Intro to fractions](/content/learn/algebra/fractions/index.html)
Draw and compare fractions, and convert to decimals
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[Multiplying fractions](/content/learn/algebra/multiplying-fractions/index.html)
What's 1/2 times 3/5? Learn the trick in this lesson!
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[Comparing fractions](/content/learn/algebra/comparing-fractions/index.html)
How to tell when fractions are equal or which is bigger
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[Cancellation](/content/learn/algebra/cancellation/index.html)
Simplifying fractions by removing common factors
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[Adding fractions](/content/learn/algebra/adding-fractions/index.html)
Add and subtract fractions using common denominators
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Dividing by a fraction is really multiplying by its reciprocal!
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[Reciprocals](/content/learn/algebra/reciprocal/index.html)
A number's multiplicative inverse is 1 over the number
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[Mixed fractions](/content/learn/algebra/mixed-numbers/index.html)
Switching between mixed and improper fractions
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[Distributing division](/content/learn/algebra/distribute-division/index.html)
The distributive law works for multiplying, but also dividing
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[When 'of' means multiply](/content/learn/algebra/multiply-of/index.html)
Evaluating fractions of numbers (like 5/7 of 210)
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Powers and roots
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Multiplying a number by itself
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[Raising to powers](/content/learn/algebra/higher-powers/index.html)
Squaring, cubing, raising to the fourth, and so on...
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[Square roots](/content/learn/algebra/integer-roots/index.html)
Work backwards to find the number that was squared
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[Roots of non-squares](/content/learn/algebra/noninteger-roots/index.html)
How to find the roots of numbers that are NOT square
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[Square roots of negatives](/content/learn/algebra/negative-roots/index.html)
Do negative numbers even have square roots?
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Cube roots, fourth roots, fifth roots, and so on...
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[PEMDAS](/content/learn/algebra/pemdas/index.html)
Order of operations, now with exponents!
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Rules for powers
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A rule for multiplying one power by another
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[Dividing powers](/content/learn/algebra/dividing-powers/index.html)
A rule for dividing one power by another
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[Raising powers to powers](/content/learn/algebra/combining-powers/index.html)
A rule for raising one power to another
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[Distributing powers](/content/learn/algebra/distribute-powers/index.html)
It works for multiplication and division, but that's it!
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[Raising to the zero](/content/learn/algebra/zero-power/index.html)
What happens when you raise a number to the zero?
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[Negative powers](/content/learn/algebra/negative-powers/index.html)
What does it mean to raise to a NEGATIVE exponent?
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[Roots as powers](/content/learn/algebra/root-powers/index.html)
Taking a root is really the same as raising to a power
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[Fractional powers](/content/learn/algebra/fractional-powers/index.html)
What does it mean to raise to the 2/3 power?
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[Distributing roots](/content/learn/algebra/splitting-roots/index.html)
Roots are also exponents, so the same rules apply!
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[Simplifying roots](/content/learn/algebra/simplifying-roots/index.html)
Getting smaller numbers under the root
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Solving equations
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Solve for unknown values using the number line
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Learn how to evaluate expressions with variables
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Adding or subtracting on both sides of equations
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Multiplying or dividing on both sides of equations
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[Cross multiplication](/content/learn/algebra/cross-multiplication/index.html)
A quick way to solve equations with fractions
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[Coefficients](/content/learn/algebra/coefficients/index.html)
Numbers in front of variables
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[Combining like terms](/content/learn/algebra/simplify/index.html)
Adding/subtracting terms with matching variables
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[Multi-step equations](/content/learn/algebra/linear-solve/index.html)
Sometimes it takes more than one step to solve!
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[Multivariable equations](/content/learn/algebra/linear-multivariable/index.html)
Solving equations when they have more than one variable
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[Unsolvable equations](/content/learn/algebra/no-solution/index.html)
Some equations have no solutions, others have plenty!
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Inequalities and simultaneous equations
[Inequalities](/content/learn/algebra/inequality-1d/index.html)
Plotting inequalities on the number line
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[Solving inequalities](/content/learn/algebra/inequality-1d-solve/index.html)
Solving and plotting multi-step inequalities
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[Negative inequalities](/content/learn/algebra/inequality-1d-negative/index.html)
What happens when you multiply by a negative
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[2 equations, 2 unknowns](/content/learn/algebra/two-equations/index.html)
Solve for both variables when you have two equations
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[2 equations, no solution](/content/learn/algebra/two-equations-singular/index.html)
Sometimes two equations have no solutions, or many!
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Coordinates
[The coordinate plane](/content/learn/algebra/cartesian/index.html)
Plotting points and finding their coordinates
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[Quadrants](/content/learn/algebra/quadrants/index.html)
The four quadrants, and the coordinates they contain
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[Finding a midpoint](/content/learn/algebra/midpoint/index.html)
Given two points, which point is exactly halfway between?
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Slope
[Slope (an introduction)](/content/learn/algebra/slope-intro/index.html)
A number that tells you the steepness of a line
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[Slope formula](/content/learn/algebra/slope-formula/index.html)
How to calculate the slope between any two points
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[Negative slopes](/content/learn/algebra/slope-negative/index.html)
Discover what it means when slope is negative
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[Zero slope](/content/learn/algebra/slope-zero/index.html)
What are the slopes of horizontal and vertical lines?
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[Find the slope of any line](/content/learn/algebra/slope-read/index.html)
Two steps that will always give you the correct slope
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[Parallel slopes](/content/learn/algebra/slope-parallel/index.html)
Explore why parallel lines have the same slope
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[Perpendicular slopes](/content/learn/algebra/slope-perpendicular/index.html)
Discover how slopes of perpendicular lines relate
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Lines
[Graphing an equation](/content/learn/algebra/first-line/index.html)
Turn an equation into your very first graph!
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[Slope-intercept form](/content/learn/algebra/slope-intercept/index.html)
Turning an equation into a line, and vice versa
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[Point-slope form](/content/learn/algebra/point-slope/index.html)
A formula for when you know the slope and coordinates
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[Reading graphs](/content/learn/algebra/read-graph/index.html)
Forget equations, let's just look at the graphs!
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[Intercepts](/content/learn/algebra/intercepts/index.html)
Figuring out where lines cross the x- and y-axes
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[Solving for intersections](/content/learn/algebra/intersection-solve/index.html)
Given two lines, can you determine where they cross?
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[Graphing absolute value](/content/learn/algebra/absolute-graph/index.html)
Exploring a graph that's not a line
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[Inequalities (2 variables)](/content/learn/algebra/inequality-2d/index.html)
Simplify inequalities with two variables and test solutions
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[Graphing inequalities](/content/learn/algebra/inequality-2d-graph/index.html)
Graph inequalities on the coordinate plane
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Polynomials
[What are polynomials?](/content/learn/algebra/polynomials-intro/index.html)
Learn about a common type of algebraic expression
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[Adding polynomials](/content/learn/algebra/polynomials-add/index.html)
Computing sums and differences of polynomials
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[Multiplying monomials](/content/learn/algebra/monomials-multiply/index.html)
Multiply and divide polynomials with one term
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[Multiplying binomials](/content/learn/algebra/binomials-multiply/index.html)
Multiply binomials together using FOIL
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[Multiplying polynomials](/content/learn/algebra/polynomials-multiply/index.html)
How to multiply polynomials with many terms
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[Difference of squares](/content/learn/algebra/difference-of-squares/index.html)
A neat trick for simplifying certain binomials
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Quadratics
[Quadratic equations](/content/learn/algebra/quadratic-equations/index.html)
Sometimes, equations can have two solutions
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[Graphing a parabola](/content/learn/algebra/first-parabola/index.html)
Plot points to draw your very first parabola
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[Graphing quadratics](/content/learn/algebra/quadratic-graph/index.html)
Every quadratic graph boils down to these 3 numbers
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[Factoring quadratics](/content/learn/algebra/quadratic-factor/index.html)
An extremely useful trick for solving some equations
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[The quadratic formula](/content/learn/algebra/quadratic-formula-proof/index.html)
A method for solving ANY quadratic equation!
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[Discriminants and roots](/content/learn/algebra/quadratic-formula-apply/index.html)
A quick way to tell how many solutions a quadratic has
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The mathematics of lines, shapes, and angles. Essential stuff for describing the world around you.
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Lines and angles
[Lines, rays, & segments](/content/learn/geometry/lines-rays/index.html)
Learn about lines, rays, and line segments
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[Angles and degrees](/content/learn/geometry/degrees/index.html)
Learn what angles are, and how to measure them
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[Right, acute, and obtuse](/content/learn/geometry/angle-names/index.html)
Learn the names for angles of all sizes
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[Parallel lines](/content/learn/geometry/parallel/index.html)
Lines that never, ever cross
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[Perpendicular lines](/content/learn/geometry/perpendicular/index.html)
Lines that cross, forming right angles
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[Naming angles](/content/learn/geometry/angle-labels/index.html)
With these rules, you know which angle you mean
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[Perpendicular bisectors](/content/learn/geometry/perpendicular-bisector/index.html)
The equidistant points also cut segments in two
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Related angles
[Combining angles](/content/learn/geometry/adding-angles/index.html)
Adding and subtracting adjacent angles
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[Complementary angles](/content/learn/geometry/complementary/index.html)
Learn about complementary and supplementary angles
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[Coterminal angles](/content/learn/geometry/coterminal-angles/index.html)
What about angles bigger than 360 degrees?
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[Vertical angles](/content/learn/geometry/vertical-angles/index.html)
Angles on opposite sides of intersecting lines
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[Corresponding angles](/content/learn/geometry/corresponding-angles/index.html)
Parallel lines form congruent angles in matching places
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[Alternate interior angles](/content/learn/geometry/alternate-interior-angles/index.html)
Congruent angles INSIDE parallel lines
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[Alternate exterior angles](/content/learn/geometry/alternate-exterior-angles/index.html)
Congruent angles OUTSIDE parallel lines
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Triangles
[Polygons](/content/learn/geometry/polygons/index.html)
A fancy name for shapes with straight sides
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[Congruence](/content/learn/geometry/congruence/index.html)
When line segments, angles, or shapes are the same
| | |
| --- | --- |
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[Triangles](/content/learn/geometry/triangles/index.html)
Introducing triangles and three different types of them
| | |
| --- | --- |
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[180 degrees in a triangle](/content/learn/geometry/triangle-180/index.html)
See if it's really true, and then prove it!
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| --- | --- |
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[Triangles by angle](/content/learn/geometry/triangle-angles/index.html)
Learn about right, acute, and obtuse triangles
| | |
| --- | --- |
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[Altitudes](/content/learn/geometry/altitudes/index.html)
Perpendicular line segments in triangles
| | |
| --- | --- |
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[Medians of triangles](/content/learn/geometry/triangle-median/index.html)
Line segments connecting vertices and midpoints
| | |
| --- | --- |
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[Isosceles triangles](/content/learn/geometry/isosceles-angles/index.html)
They have two equal sides, but what about their angles?
| | |
| --- | --- |
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[Triangle inequality](/content/learn/geometry/triangle-inequality/index.html)
The rules a triangle's side lengths always follow
| | |
| --- | --- |
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[Big angles, longer sides](/content/learn/geometry/triangle-compare/index.html)
In triangles, sides and their opposite angles are related!
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| --- | --- |
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Triangle congruence and similarity
[Similarity](/content/learn/geometry/similarity/index.html)
When they have the same shape, but different sizes
| | |
| --- | --- |
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[Similar ratios](/content/learn/geometry/similar-ratios/index.html)
Use similarity to find unknown side lengths!
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| --- | --- |
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[SSS Postulate](/content/learn/geometry/triangles-sss/index.html)
Using sides to see if triangles are congruent
| | |
| --- | --- |
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[SAS Postulate](/content/learn/geometry/triangles-sas/index.html)
Congruence check using two sides and the angle between
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| --- | --- |
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[ASA Postulate](/content/learn/geometry/triangles-asa/index.html)
Congruence check using two angles and the side between
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| --- | --- |
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[AAS Postulate](/content/learn/geometry/triangles-aas/index.html)
The final congruence check for triangles
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| --- | --- |
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[AA Postulate (Similarity)](/content/learn/geometry/triangles-aa/index.html)
Triangles are similar when they have matching angles
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| --- | --- |
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[SSA (ambiguous case)](/content/learn/geometry/triangles-ssa/index.html)
Depending on the sides, you can have 0, 1, or 2 triangles!
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| --- | --- |
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Polygons and quadrilaterals
[Quadrilaterals](/content/learn/geometry/quads/index.html)
Learn about rectangles, rhombi, and more!
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| --- | --- |
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[Regular polygons](/content/learn/geometry/regular-polygons/index.html)
Polygons with equal sides and angles
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| --- | --- |
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[Perimeter](/content/learn/geometry/perimeter/index.html)
Tricks for finding the distance around a shape
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| --- | --- |
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[Angles in polygons](/content/learn/geometry/polygon-180/index.html)
Find a formula for the sum of the angles in any polygon
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| --- | --- |
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[Parallelogram angles](/content/learn/geometry/parallelogram-angles/index.html)
Opposite angles are congruent in parallelograms
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| --- | --- |
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[Parallelogram sides](/content/learn/geometry/parallelogram-sides/index.html)
Opposite sides are congruent in parallelograms
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| --- | --- |
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[Paralleogram diagonals](/content/learn/geometry/parallelogram-diagonals/index.html)
In parallelograms, diagonals always bisect each other
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| --- | --- |
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[Rectangle diagonals](/content/learn/geometry/rectangle-diagonals/index.html)
Rectangles always have two congruent diagonals
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| --- | --- |
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[Rhombus diagonals](/content/learn/geometry/rhombus-diagonals/index.html)
In rhombi, the diagonals are always perpendicular
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| --- | --- |
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[Trapezoid angles](/content/learn/geometry/trapezoid-angles/index.html)
Supplementary pairs of angles in trapezoids
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| --- | --- |
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Area of polygons
[Intro to area](/content/learn/geometry/area/index.html)
Measuring how much space is inside a shape
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| --- | --- |
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[Rectangle area](/content/learn/geometry/rectangle-area/index.html)
Discover the formula for the area of a rectangle
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| --- | --- |
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[Parallelogram area](/content/learn/geometry/parallelogram-area/index.html)
Discover the formula for the area of a parallelogram
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| --- | --- |
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[Triangle area](/content/learn/geometry/triangle-area/index.html)
Discover a formula for the area of any triangle
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| --- | --- |
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[Trapezoid area](/content/learn/geometry/trapezoid-area/index.html)
Discover the formula for the area of a trapezoid
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| --- | --- |
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[Rhombus area](/content/learn/geometry/rhombus-area/index.html)
Find a rhombus' area using its diagonals
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| --- | --- |
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The Pythagorean theorem
[Pythagorean theorem](/content/learn/geometry/pythagorean-theorem/index.html)
How the sides of right triangles are related
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| --- | --- |
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[Pythagorean triples](/content/learn/geometry/pythagorean-triples/index.html)
When whole numbers are the sides of right triangles
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| --- | --- |
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[Generating triples](/content/learn/geometry/pythagorean-triples-generate/index.html)
Ways to write out every last Pythagorean triple
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| --- | --- |
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[Distance formula](/content/learn/geometry/distance-formula/index.html)
Find the distance between any two points
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| --- | --- |
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[Equilateral area](/content/learn/geometry/equilateral-area/index.html)
Finding the area of equilateral and isosceles triangles
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| --- | --- |
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[Heron's formula](/content/learn/geometry/herons-formula/index.html)
Another way to find the area of a triangle
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| --- | --- |
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[Proving Heron's formula](/content/learn/geometry/herons-formula-proof/index.html)
You might know the formula, but where does it come from?
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| --- | --- |
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Circles, ellipses, and their areas
[Circles](/content/learn/geometry/circles/index.html)
An intro to circles, radii, diameters, and chords
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| --- | --- |
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[Circumference and Pi](/content/learn/geometry/circumference/index.html)
Find the distance around a circle (and then eat some pi)
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| --- | --- |
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[Size of the Earth](/content/learn/geometry/earth-size/index.html)
Use shadows to measure the Earth's circumference!
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| --- | --- |
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[Ellipses](/content/learn/geometry/ellipse/index.html)
What you get when you "stretch" a circle
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| --- | --- |
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[Area of a circle](/content/learn/geometry/circle-area/index.html)
Using circumference to find a circle's area
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| --- | --- |
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[Cavalieri's principle](/content/learn/geometry/cavalieri-2d/index.html)
Comparing shapes to find areas of the unusual ones
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| --- | --- |
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[Ellipse area](/content/learn/geometry/ellipse-area/index.html)
Calculate how many people can fit on the Ellipse in DC
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| --- | --- |
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[Areas of complex shapes](/content/learn/geometry/combining-areas/index.html)
Add and subtract the ares of simpler shapes!
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| --- | --- |
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Angles in circles
[Central angles and arcs](/content/learn/geometry/central-angle/index.html)
As you'll see, there are 360 degrees in every circle
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| --- | --- |
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[Inscribed angles](/content/learn/geometry/inscribed-angle/index.html)
Discover how inscribed angles are related to central angles!
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| --- | --- |
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[Inscribing the diameter](/content/learn/geometry/inscribed-diameter/index.html)
Prove that inscribed angles drawn to diameters are right
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| --- | --- |
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[Arc length](/content/learn/geometry/arc-degrees/index.html)
Finding a formula for the length of any arc
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| --- | --- |
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[Sector area](/content/learn/geometry/sector-degrees/index.html)
How to find the area of any slice of a circle
| | |
| --- | --- |
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Lines in circles
[Secant and tangent lines](/content/learn/geometry/circle-lines/index.html)
Some lines cross circles twice, others touch them only once
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| --- | --- |
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[Congruent tangents](/content/learn/geometry/congruent-tangents/index.html)
Prove that tangents from the same point are congruent
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| --- | --- |
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[Circumscribed angles](/content/learn/geometry/circumscribed-angle/index.html)
Discover how angles between tangents are related to arcs
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| --- | --- |
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[Parallel chords](/content/learn/geometry/parallel-chords/index.html)
Prove that the arcs between them are always congruent
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| --- | --- |
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[Intersecting chords](/content/learn/geometry/chord-product/index.html)
Discover a rule for how intersecting chords relate
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| --- | --- |
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[Cyclic quadrilaterals](/content/learn/geometry/cyclic-quad/index.html)
See how their opposite angles are related!
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| --- | --- |
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[Intersecting secants](/content/learn/geometry/secant-product/index.html)
Like chords, intersecting secants are also related!
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| --- | --- |
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[Inscribed circles](/content/learn/geometry/inscribed-circle/index.html)
Calculate the radius of any inscribed circle
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| --- | --- |
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Volume
[Intro to solids](/content/learn/geometry/shapes-3d/index.html)
Learn the names and features of 3D shapes
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| --- | --- |
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[Rectangular prisms](/content/learn/geometry/prism-volume/index.html)
Discover how to find the volume of any box!
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| --- | --- |
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[Prism volume](/content/learn/geometry/other-prism-volume/index.html)
Find the volume of prisms and cylinders
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| --- | --- |
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[Cavalieri's Principle (3D)](/content/learn/geometry/cavalieri-3d/index.html)
Instead of matching widths, you'll be matching areas!
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| --- | --- |
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[Pyramid volume](/content/learn/geometry/pyramid-volume/index.html)
Starting with a cube, discover the pyramid volume formula
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| --- | --- |
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[Cone volume](/content/learn/geometry/cone-volume/index.html)
Find the volume of any cone, and learn about slant height
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| --- | --- |
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[Sphere volume](/content/learn/geometry/sphere-volume/index.html)
Use Cavalieri's principle to find the volume of a sphere
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| --- | --- |
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Surface area
[Prism surface area](/content/learn/geometry/prism-surface/index.html)
Learn why ice is commonly shaped into cubes
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| --- | --- |
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[Pyramid surface area](/content/learn/geometry/pyramid-surface/index.html)
Find a pyramid's surface area using squares and triangles
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| --- | --- |
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[Cylinder surface area](/content/learn/geometry/cylinder-surface/index.html)
Unroll any cylinder to find its surface area!
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| --- | --- |
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[Cone surface area](/content/learn/geometry/cone-surface/index.html)
Discover and use the formula for a cone's surface area!
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| --- | --- |
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[Sphere surface area](/content/learn/geometry/sphere-surface/index.html)
Find the the total area of a sphere's curved surface
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| --- | --- |
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[Internal diagonals](/content/learn/geometry/internal-diagonal/index.html)
What's the distance between opposite corners of a cube?
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| --- | --- |
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Transformations
[Translation](/content/learn/geometry/translation/index.html)
Moving points and shapes in the coordinate plane
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| --- | --- |
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[Rotation](/content/learn/geometry/rotation/index.html)
Rotating points and shapes around the origin
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| --- | --- |
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[Reflection](/content/learn/geometry/reflection/index.html)
Flipping across different axes (and the origin)
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| --- | --- |
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[Dilation](/content/learn/geometry/stretch/index.html)
Stretching shapes in one or two directions
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| --- | --- |
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[Preserving congruence](/content/learn/geometry/preserving-congruence/index.html)
See which transformations keep things congruent
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| --- | --- |
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[Symmetry](/content/learn/geometry/symmetry/index.html)
When reflection or rotation doesn't change anything
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| --- | --- |
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Geometric optics
[Why light bends](/content/learn/geometry/refraction/index.html)
Using Fermat's principle to understand refraction
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[Rainbows explained](/content/learn/geometry/rainbow/index.html)
Use refraction to understand rainbows and their features
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| --- | --- |
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Trigonometry helps you understand any topic that involves distances, angles, or waves. The trig functions (sin, cos, and tan) show up all over science and engineering.
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**COMPLETION**
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Radians
[What's a "radian"?](/content/learn/trigonometry/radians/index.html)
Discover another way to measure angles.
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| --- | --- |
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[Radians and degrees](/content/learn/trigonometry/radians-conversion/index.html)
How to switch back and forth between units for angles
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[Lengths of circular arcs](/content/learn/trigonometry/arc-radian/index.html)
A formula for arc length in terms of radius and angle
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| --- | --- |
| | Start lesson |
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[Sectors](/content/learn/trigonometry/sector-area/index.html)
Learn what a sector is, and a formula for finding its area
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| --- | --- |
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Trig functions
[Sides of right triangles](/content/learn/trigonometry/side-names/index.html)
Your friendly hypotenuses, opposites, and adjacents
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| --- | --- |
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[Sine](/content/learn/trigonometry/sine/index.html)
Your very first trig function
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[Cosine](/content/learn/trigonometry/cosine/index.html)
Along with sine, cosine is a fundamental trig function
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| --- | --- |
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[Tangent](/content/learn/trigonometry/tangent/index.html)
Another important trig function (like sine and cosine)
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| --- | --- |
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[Components (and cops)](/content/learn/trigonometry/components/index.html)
Find legs of right triangles, and don't get pulled over!
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[Sec, Csc, and Cot](/content/learn/trigonometry/secant/index.html)
Secant and friends (three more trig functions)
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Special angles
[45 degrees](/content/learn/trigonometry/trig-45/index.html)
Calculate the sine, cosine, and tangent of 45 degrees
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| --- | --- |
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[30/60 degrees](/content/learn/trigonometry/trig-30/index.html)
Calculate the sine, cosine, and tangent of 30 and 60 degrees
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[0/90 degrees](/content/learn/trigonometry/trig-90/index.html)
Calculate the sine, cosine, and tangent of 0 and 90 degrees
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The unit circle
[Trig for larger angles](/content/learn/trigonometry/larger-angles/index.html)
What's sin(250)? Use the unit circle to tackle bigger angles
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[Trig for negative angles](/content/learn/trigonometry/negative-angles/index.html)
Using the unit circle for trig with negative angles
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[Trig for coterminals](/content/learn/trigonometry/coterminal-trig/index.html)
How trig functions are related for coterminal angles
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Inverse trig functions
[Inverse sine](/content/learn/trigonometry/inverse-sin/index.html)
A function that takes you from side ratios to angles
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[Inverse cosine](/content/learn/trigonometry/inverse-cos/index.html)
Another inverse trig function
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[Inverse tangent](/content/learn/trigonometry/inverse-tan/index.html)
And one last inverse trig function!
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Trig identities
[Trig identities](/content/learn/trigonometry/trig-identities-intro/index.html)
The tools for simplifying trig expressions
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[Addition identities](/content/learn/trigonometry/trig-identities-addition/index.html)
Simplify trig functions of sums
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[Negative angle identities](/content/learn/trigonometry/trig-identities-negative/index.html)
Simplify trig functions of negative angles
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[Subtraction identities](/content/learn/trigonometry/trig-identities-difference/index.html)
Simplify trig functions of differences
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[Double angle identities](/content/learn/trigonometry/trig-identities-double/index.html)
Trig functions of twice an angle
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[Triple angle identities](/content/learn/trigonometry/trig-identities-triple/index.html)
Trig functions of three times an angle
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[Pythagorean identities](/content/learn/trigonometry/trig-identities-pythagorean/index.html)
Relating squares of trig functions
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[Half angle identities](/content/learn/trigonometry/trig-identities-half/index.html)
Trig functions of half an angle
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Triangle formulas
[Law of sines](/content/learn/trigonometry/law-of-sines/index.html)
Relating angles and opposite sides for any triangle
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| --- | --- |
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[Triangulation](/content/learn/trigonometry/triangulation/index.html)
Real-world application of the law of sines to find distances
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[Law of cosines](/content/learn/trigonometry/law-of-cosines/index.html)
Relating three sides and an angle for any triangle
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| --- | --- |
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[Triangle area: SAS](/content/learn/trigonometry/triangle-area-sas/index.html)
Find a triangle's area using 2 sides and the angle between
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| --- | --- |
| | Start lesson |
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Take the next step in Algebra! Here we'll introduce the most common functions you're likely to see, and different ways to describe functions.
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Real numbers
[Integers](/content/learn/precalculus/integers/index.html)
Whole numbers, positives, and negatives
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[Rationals](/content/learn/precalculus/rationals/index.html)
Numbers that are quotients of integers
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[Irrationals](/content/learn/precalculus/irrationals/index.html)
Numbers that are NOT quotients of integers
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| | Start lesson |
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[Real numbers](/content/learn/precalculus/reals/index.html)
All the rationals and the irrationals
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| | Start lesson |
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Imaginary and complex numbers
[Imaginary numbers](/content/learn/precalculus/imaginary/index.html)
Their squares are negative!
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| --- | --- |
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[Working with imaginaries](/content/learn/precalculus/imaginary-operations/index.html)
Add, subtract, multiply, and divide imaginary numbers
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| --- | --- |
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[Complex numbers](/content/learn/precalculus/complex-numbers/index.html)
Combining the real and the imaginary
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| --- | --- |
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[The complex plane](/content/learn/precalculus/complex-plane/index.html)
A way to graph complex numbers
| | |
| --- | --- |
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[Powers of _i_](/content/learn/precalculus/powers-of-i/index.html)
Raising _i_ to positive and negative integer powers
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| | Start lesson |
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Functions
[Relations](/content/learn/precalculus/relations/index.html)
Sets of (x,y) coordinates
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| --- | --- |
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[Functions](/content/learn/precalculus/functions/index.html)
Relations where each input gives exactly one output
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[Functional notation](/content/learn/precalculus/functional-notation/index.html)
Explore what f(x) means, and evaluate functions
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[Continuity and smoothness](/content/learn/precalculus/continuity/index.html)
Some functions end and others keep going
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[Describing functions](/content/learn/precalculus/describing-functions/index.html)
Make your own functions, and live to tell the tale
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[Concavity](/content/learn/precalculus/concavity/index.html)
Math-talk for "curvy"
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[Odd and even functions](/content/learn/precalculus/odd-even/index.html)
Turns out functions can be "odd" and "even" too
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Exponents
Logarithms
Playing with functions
[Piecewise functions](/content/learn/precalculus/piecewise/index.html)
Franken-functions. They're alive!
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[Compositions](/content/learn/precalculus/compositions/index.html)
Functions of functions
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Conic sections
Rational functions
Polar functions
The mathematics of change. And it'll use just about every branch of math you've learned before it.
**SUBJECT**
**COMPLETION**
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Limits
[Limits to infinity](/content/learn/calculus/horizontal-asymptotes/index.html)
What happens to functions as _x_ gets really, really big?
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[Vertical limits](/content/learn/calculus/vertical-asymptotes/index.html)
Sometimes _y_ goes off to infinity
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[Finite limits](/content/learn/calculus/finite-limits/index.html)
Limits when both _x_ and _y_ stay finite
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[One-sided limits](/content/learn/calculus/one-sided-limits/index.html)
Limits that come from only the left or right side
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[Continuity (for real)](/content/learn/calculus/discontinuities/index.html)
Dive deeper into continuity, using one-sided limits
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[Splitting limits](/content/learn/calculus/limit-rules/index.html)
Tricks for simplifying limits (and when they don't work!)
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Derivatives
[Tangent lines](/content/learn/calculus/tangent-lines/index.html)
Finding the "slope" of a curve
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[Drawing derivatives](/content/learn/calculus/drawing-derivatives/index.html)
Learn what a derivative is, and draw your own
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Integrals
Series
The math of data collection and analysis. Very useful for finding trends and making predictions!
**SUBJECT**
**COMPLETION**
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Sensitivity analysis
[Sensitivity and specificity](/content/learn/statistics/sensitivity/index.html)
Quantifying whether tests for diseases are any good
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[Predictive value](/content/learn/statistics/predictive-value/index.html)
If you test positive/negative, what are your chances?
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[Cutoffs and ROCs](/content/learn/statistics/test-cutoff/index.html)
Sensitivity vs. specifity, cutoff selection, and ROC curves
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[Prevalence](/content/learn/statistics/prevalence/index.html)
How rare a disease is, and how it affects PPV and NPV
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Distributions
Regression analysis
Hypothesis testing
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