12/24/2015 Geometry Section 9.3 The Converse of the Pythagorean Theorem.

04/21/23

Geometry

Section 9.3The Converse of the Pythagorean Theorem

right

right

If it is a right triangle, it will satisfy the Pythagorean Theorem2 2 2a b c

Note: c is always the longest side

2 2224 8 6 8 15 576 384 960

960 960 The triangle is a right triangle

2 2 2a b c

2 2 233 56 65 1089 3136 4225

4225 4225

The triangle is a right triangle

22 210 2 38 16

100 152 256 252 256

The triangle is not a right triangle

acute

acute

obtuse

obtuse

2 2 2If , then the triangle is acutea b c 2 2 2If , then the triangle is obtu e sa b c 2 2 2If , then the triangle is righta b c

2 2 228 40 48

784 1600 2304

2384 2304acute

2 2 25.7 12.2 13.9

32.49 148.84 193.21

181.33 193.21obtuse

2 2 2If , then the triangle is acutea b c 2 2 2If , then the triangle is obtu e sa b c 2 2 2If , then the triangle is righta b c

2 2 216 30 34256 900 1156

1156 1156

Right triangle

A triangle can’t be formed

In order for a triangle to be formed,the sum of any two sides must be

larger than the third side.

• End

• Assignment:– Pg.546 # 8-25,26,28,30,47-53

04/21/23

Geometry

Section 9.3The Converse of the Pythagorean Theorem

2 2 2If , then the triangle is acutea b c 2 2 2If , then the triangle is obtu e sa b c 2 2 2If , then the triangle is righta b c

2 2 2If , then the triangle is acutea b c 2 2 2If , then the triangle is obtu e sa b c 2 2 2If , then the triangle is righta b c