Geometry
The mathematics of lines, shapes, and angles. Essential stuff for describing the world around you.
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1. Lines and angles
Learn about lines, rays, and line segments
Learn what angles are, and how to measure them
Learn the names for angles of all sizes
Lines that never, ever cross
Lines that cross, forming right angles
With these rules, you know which angle you mean
The equidistant points also cut segments in two
2. Related angles
Adding and subtracting adjacent angles
Learn about complementary and supplementary angles
What about angles bigger than 360 degrees?
Angles on opposite sides of intersecting lines
Parallel lines form congruent angles in matching places
Congruent angles INSIDE parallel lines
Congruent angles OUTSIDE parallel lines
3. Triangles
A fancy name for shapes with straight sides
When line segments, angles, or shapes are the same
Introducing triangles and three different types of them
See if it's really true, and then prove it!
Learn about right, acute, and obtuse triangles
Perpendicular line segments in triangles
Line segments connecting vertices and midpoints
They have two equal sides, but what about their angles?
The rules a triangle's side lengths always follow
In triangles, sides and their opposite angles are related!
4. Triangle congruence and similarity
When they have the same shape, but different sizes
Use similarity to find unknown side lengths!
Using sides to see if triangles are congruent
Congruence check using two sides and the angle between
Congruence check using two angles and the side between
The final congruence check for triangles
Triangles are similar when they have matching angles
Depending on the sides, you can have 0, 1, or 2 triangles!
5. Polygons and quadrilaterals
Learn about rectangles, rhombi, and more!
Polygons with equal sides and angles
Tricks for finding the distance around a shape
Find a formula for the sum of the angles in any polygon
Opposite angles are congruent in parallelograms
Opposite sides are congruent in parallelograms
In parallelograms, diagonals always bisect each other
Rectangles always have two congruent diagonals
In rhombi, the diagonals are always perpendicular
Supplementary pairs of angles in trapezoids
6. Area of polygons
Measuring how much space is inside a shape
Discover the formula for the area of a rectangle
Discover the formula for the area of a parallelogram
Discover a formula for the area of any triangle
Discover the formula for the area of a trapezoid
Find a rhombus' area using its diagonals
7. The Pythagorean theorem
How the sides of right triangles are related
When whole numbers are the sides of right triangles
Ways to write out every last Pythagorean triple
Find the distance between any two points
Finding the area of equilateral and isosceles triangles
Another way to find the area of a triangle
You might know the formula, but where does it come from?
8. Circles, ellipses, and their areas
An intro to circles, radii, diameters, and chords
Find the distance around a circle (and then eat some pi)
Use shadows to measure the Earth's circumference!
What you get when you "stretch" a circle
Using circumference to find a circle's area
Comparing shapes to find areas of the unusual ones
Calculate how many people can fit on the Ellipse in DC
Add and subtract the ares of simpler shapes!
9. Angles in circles
As you'll see, there are 360 degrees in every circle
Discover how inscribed angles are related to central angles!
Prove that inscribed angles drawn to diameters are right
Finding a formula for the length of any arc
How to find the area of any slice of a circle
10. Lines in circles
Some lines cross circles twice, others touch them only once
Prove that tangents from the same point are congruent
Discover how angles between tangents are related to arcs
Prove that the arcs between them are always congruent
Discover a rule for how intersecting chords relate
See how their opposite angles are related!
Like chords, intersecting secants are also related!
Calculate the radius of any inscribed circle
11. Volume
Learn the names and features of 3D shapes
Discover how to find the volume of any box!
Find the volume of prisms and cylinders
Instead of matching widths, you'll be matching areas!
Starting with a cube, discover the pyramid volume formula
Find the volume of any cone, and learn about slant height
Use Cavalieri's principle to find the volume of a sphere
12. Surface area
Learn why ice is commonly shaped into cubes
Find a pyramid's surface area using squares and triangles
Unroll any cylinder to find its surface area!
Discover and use the formula for a cone's surface area!
Find the the total area of a sphere's curved surface
What's the distance between opposite corners of a cube?
13. Transformations
Moving points and shapes in the coordinate plane
Rotating points and shapes around the origin
Flipping across different axes (and the origin)
Stretching shapes in one or two directions
See which transformations keep things congruent
When reflection or rotation doesn't change anything
14. Geometric optics
Using Fermat's principle to understand refraction
Use refraction to understand rainbows and their features
