1. Chapter 10 Vocabulary 1.) hypotenuse 2.) leg 3.) Pythagorean Theorem
4.)

2. 10-1 The Pythagorean Theorem and its Converse
Algebra 1

3. The Pythagorean Theorem
states, if a and b are the measures of the legs of a right triangle and c is the measure of the hypotenuse, then

4. Example 1
Find the missing length of the right triangle if a & b are the lengths of the legs and c is the length of the hypotenuse.
a.) a=5, b=7,
b.) b=9, c=16,

5. Example 2 Find each missing length. a.)x, 1, b.)x, x-6, 30
B=/84 or 9.17

6. If-Then Statements
State the hypothesis (if) and the conclusion (then) of the statement.
If a polygon is a square, then it is a parallelogram.
The converse of a conditional switches the hypothesis and the conclusion which may or may not be true.

7. Converse to the Pythagorean Theorem
If a triangle has side lengths a, b, and c such that then the triangle is a right triangle.

8. Example 3, a
Determine whether the given lengths are sides of a right triangles.
a.) a = 8, b = 9, c = 11 no

9. Example 3, b
Determine whether the following side measures would form right triangles.
b.) a = 13, b = 84, c = 85
yes

10. Using the Pythagorean Theorem
A ladder 8 m long is resting against a building. The bottom of the ladder is 3 m from the wall. To the nearest tenth, how far up the wall does the ladder reach?
7.4 m

11. Pythagorean Triple -
Any set of 3 positive integers that satisfies the equation

12. Ex. 4 Determine whether each set of numbers is a Pythagorean Triple.

13. Assignment