8-1 The Pythagorean Theorem and Its Converse
Objective
To use the Pythagorean Theorem and its converse
Dynamic Activity
Pythagorean Theorem
Lesson Vocabulary
- Pythagorean triple
The equations in the Solve It demonstrate an important relationship in right triangles called the Pythagorean Theorem. This theorem is named for Pythagoras, a Greek mathematician who lived in the 500s B.C. We now know that the Babylonians, Egyptians, and Chinese were aware of this relationship before its discovery by Pythagoras. There are many proofs of the Pythagorean Theorem. You will see one proof in this lesson and others later in the book.
Essential Understanding If you know the lengths of any two sides of a right triangle, you can find the length of the third side by using the Pythagorean Theorem.
Take Note Theorem 8-1: Pythagorean Theorem
Theorem
If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
If …
Then …
You will prove Theorem 8-1 in Exercise 49.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs