9.3 The converse of the Pythagorean thm

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9.3 The converse of the Pythagorean thm. How do I use the Converse of the Pythagorean Theorem to solve problems? How do I use side lengths to classify triangles by their angle measures?. Thm 9.5 converse of the Pythagorean thm. If c 2 =a 2 +b 2 , then Δ ABC is a right Δ. B. c. a. A. C.

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### 9.3 The converse of the Pythagorean thm

How do I use the Converse of the Pythagorean Theorem to solve problems? How do I use side lengths to classify triangles by their angle measures?

Thm 9.5converse of the Pythagorean thm
• If c2=a2+b2, then Δ ABC is a right Δ.

B

c

a

A

C

b

ExampleAre the Δs right Δs?

7

10

6

13.4

12

13.42=102+72

179.56=100+49

179.56=149

36*5=36+144

180=180

Thm 9.6
• If c2<a2+b2, then the Δ is acute.

A

c

b

C

B

a

Thm 9.7
• If c2>a2+b2, then the Δ is obtuse.

A

c

b

B

a

C

Example Can the given side lengths form a Δ and if so, what kind of Δ would it be?

3.2, 4.8, 5.1

Yes, they form a Δ (by the Δinequal. Thm)

3.2+4.8>5.1; 4.8+5.1>3.2; and 3.2+5.1>4.8

What kind of Δ?

5.12___4.82+3.22

26.01___23.04+10.24

26.01___33.28

acute

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