Lesson 9-5 Pages 460-464

The Pythagorean Theorem

Lesson Check 9-4

What you will learn!1. How to use the Pythagorean

Theorem to find the length of a side of a right triangle.

2. Use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

LegsLegsHypotenuseHypotenusePythagorean TheoremPythagorean TheoremSolving a right triangleSolving a right triangleConverseConverse

What you really need to know!

Pythagorean Theorem

If a triangle is a right triangle, then the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

What you really need to know!

ac

b

a2 + b2 = c2

Example:

35

432 + 42 = 52

9 + 16 = 2525 = 25

Example 1:

Find the length of the hypotenuse of the right triangle.

20ft

c ft21ft

a2 + b2 = c2

212 + 202 = c2

441 + 400 = c2

841 = c2

29 = c

Example 2:

Find the length of the leg of the right triangle.

b m

11 m

8 m

a2 + b2 = c2

82 + b2 = 112

64 + b2 = 121b2 = 57

b ≈ 7.5 m

A building is 10 feet tall. A ladder is positioned against the building so that the base of the ladder is 3 feet from the building. How long is the ladder?

AA 12.412.4 BB 10.410.4 CC 10.010.0 DD 14.914.9

3 ft

10 ft

Example 3:

Example 4:

The measure of three sides of a triangle are given. Determine whether the triangle is a right triangle.

48 ft48 ft 60 ft60 ft 78 ft78 ft

482 + 602 ?=? 782

NO!

Example 4a:

The measure of three sides of a triangle are given. Determine whether the triangle is a right triangle.

24 ft24 ft 70 ft70 ft 74 ft74 ft

242 + 702 ?=? 742

YES!

Page 462

Guided Practice

#’s 3-9

Pages 460-462 with someone at home and

study examples!

Read:

Homework: Pages 463-464

#’s 10-36 even, 39, 40, and 44-52

Lesson Check 9-5

Page

746

Lesson 9-5

Lesson Check 9-5

Homework: Pages 463-464

#’s 10-21, 26-31, 34, 39, 40, 44-52

Lesson Check 9-5