9.3 The converse of the 9.3 The converse of the Pythagorean thmPythagorean thm

How do I use the Converse of How do I use the Converse of the Pythagorean Theorem to the Pythagorean Theorem to

solve problems? How do I use solve problems? How do I use side lengths to classify triangles side lengths to classify triangles

by their angle measures?by their angle measures?

Thm 9.5Thm 9.5converse of the Pythagorean thmconverse of the Pythagorean thm• If cIf c22=a=a22+b+b22, then , then ΔΔ ABC is a right ABC is a right ΔΔ..

A

B

C

a

b

c

ExampleExampleAre the Are the ΔΔs right s right ΔΔs?s?

566

12

180=180

222 126)56(

107

13.4

13.413.422=10=1022+7+722

179.56=149179.56=14936*5=36+144

179.56=100+49179.56=100+49

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

A

BCa

bc

Thm 9.7

• If c2>a2+b2, then the Δ is obtuse.A

B

Ca

b

c

Example Example Can the given side lengths form a Can the given side lengths form a ΔΔ

and if so, what kind of and if so, what kind of ΔΔ would it be would it be??

3.2, 4.8, 5.13.2, 4.8, 5.1

Yes, they form a Yes, they form a ΔΔ (by the (by the ΔΔ inequal. Thm) inequal. Thm)

3.2+4.8>5.1; 4.8+5.1>3.2; and 3.2+5.1>4.83.2+4.8>5.1; 4.8+5.1>3.2; and 3.2+5.1>4.8

What kind of What kind of ΔΔ??

5.15.122___4.8___4.822+3.2+3.222

26.01___23.04+10.2426.01___23.04+10.24

26.01_26.01____33.28_33.28

acuteacute

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AssignmentWS 9.3B #2-16 even, 17,18WS 9.3B #2-16 even, 17,18