Pythagorean Theorem and it’s converse

Sec: 8.1Sol: G.8

Theorem 7.4: 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 4

Example

A

B

C

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

Lesson 7-2: The Pythagorean Theorem 5

Pythagorean Theorem : Examples1. A=8, B= 15, Find C

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

A

B

C

C = 17

C = 25

Solve for x

x 3

5

1.

2. x 4

6

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?

Theorem 7.5 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 triangle:1. 9

15

343 2.

14 2

2 26

Determine if the triangle is Right, Acute, or ObtuseRight: a2 + b2 = c2

Acute: a2 + b2 > c2

Obtuse: a2 + b2 < c2

Try these:

1) a=10, b=15, c=202) a=2, b=5, c=63) a=12, b=16, c=204) a=11, b=12, c=145) a=2, b=3, c=46) a=1, b=7, c=77) a=90, b=120, c=150

Suggested AssignmentsClasswork: Workbook Pg 203 1-15,24-

27,29,30 Handout

Homework: pg 495-497 2-12e, 16-22e (solve no Radical) 28-32e