- Topics At a Glance
- Basic Shapes & Angles
- Angles
- Parallel Lines & Transversals
- Polygons
- Triangles
- Quadrilaterals
- Angles in a Polygon
- Circles
- Similar Figures
- Perimeter & Circumference
- Area (Polygon, Triangle, Circle, Square)
- Area Formulas
- Area of Irregular Shapes
- 3D Objects (Prisms, Cylinders, Cones, Spheres)
- Volume of Prisms & Cylinders
- Volume of Pyramids & Cones
- Volume of Spheres
- Surface Area
**Pythagorean Theorem**

A long time ago, in ancient Greece, a brilliant guy named Pythagoras discovered something pretty amazing and useful.

In a * right triangle *the

**Legs**(a and b): the sides of the triangle adjacent to the right angle. They don't need to be the same length in order for this theorem to work**Hypotenuse**(c): the side of the triangle opposite the right angle

So, let's break this down. If you **square each side of the triangle**, the sum of the areas of the two legs squared is equal to the hypotenuse squared.

Here you can see it with numbers:

The area of the two smaller squares is and

The area of the larger square is equal to

If you add the two smaller areas together, you get the area of the square of the hypotenuse

*Look Out**: Do not attempt this with obtuse or acute triangles! This awesome theorem only works for right triangles!*

Example 1

Find the missing side of this triangle. | The length of the hypotenuse is missing, and we are given the lengths of the legs. |

Example 2

Find the length of the missing side of this right triangle. | The length of a leg is missing, and we are given the lengths of the other leg and the hypotenuse. |

Example 3

Is a triangle with sides lengths of 4 cm, 7 cm, and 8 cm a right triangle? | If it is a right triangle, then the sum of the squares of the two smaller sides will equal the square of the largest side. |

Exercise 1

Find the length of the missing side of this triangle.

Exercise 2

Find the length of the missing side of this triangle.

Exercise 3

Could a right triangle have side lengths of 29, 21, and 20 inches?