Pythagorean Theorem and its converse

Pythagorean Theorem and its converse

Section 8-1

Pythagorean TheoremIn a right triangle the sum of the squares of the

measures of the legs equals the square of the measure of the hypotenuse.

a2 + b2 = c2

ac

b

Leg

Leg

Hypotenuse

Lesson 7-2: The Pythagorean Theorem 8

Example 1

A

B

C

In the following figure if A = 8 and B = 6, Find C.

Lesson 7-2: The Pythagorean Theorem 9

Pythagorean Theorem : Examples 2 and 32. A=8, B= 15, Find C

3. A=7, B= 24, Find C

A

B

C

C = 17

C = 25

Solve for x

x 3

5

4.

5. x 4

6

Word problems ex. 6The foot of a ladder is 6 feet from a wall. If

the top of the ladder rests 8 feet up a wall, how long is the ladder?

Example 7

Randy made a ramp for his dog to get into his truck. The ramp is 6 ft long and the bed of the truck is 3ft above the ground. Approximately how far from the back of the truck does the ramp touch the ground?

Example 8Donna’s TV screen is 20 inches long. If the

diagonal measures 25 inches, what is the width of the tv screen?

Example 9Town A is 9 miles from town B, and 12 miles

from town C. A road connects towns B and C directly. Find the length of this road. Angle B is the right angle.

Converse of the Pythagorean theoremIf the sum of the square of the measures of two

sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.

If a2 + b2 = c2, then ∆ABC is a right triangle.

a

C

B

A b

c

Tell whether it is a right triangle:10.

9

15

343 11.

14 2

2 26