Converse of the Pythagorean Theorem 9.3 c = 10 c = 5.

Converse of the Pythagorean Theorem9.3

c = 10 c = 5

356 2 89c 160 4 10c

196 14b

Converse of the Pythagorean Theorem9.3

Chapter 9Right Triangles and Trigonometry

Section 9.3

Converse of the Pythagorean Theorem

USE THE CONVERSE OF THE PYTHAGOREAN THEOREM

USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE

Converse of the Pythagorean Theorem9.3

THEOREM

A

BC

USE THE CONVERSE OF THE PYTHAGOREAN THEOREM

THEOREM 9.5 Converse of the Pythagorean Theorem

c 2 = a

2 + b 2

b

ac

In a triangle, if c2 = a2 + b2, then the triangle is a right triangle

ABC is a right Triangle

Converse of the Pythagorean Theorem9.3

THEOREM

AB

C

USE THE CONVERSE OF THE PYTHAGOREAN THEOREM

THEOREM 9.6

c 2 < a

2 + b 2

In a triangle, if c2 < a2 + b2, then the triangle is acute

ABC is acuteba

c

Converse of the Pythagorean Theorem9.3

THEOREM

AC

B

b

ac

USE THE CONVERSE OF THE PYTHAGOREAN THEOREM

THEOREM 9.7

c 2 > a

2 + b 2

In a triangle, if c2 > a2 + b2, then the triangle is obtuse

ABC is obtuse

Converse of the Pythagorean Theorem9.3

Converse of the Pythagorean TheoremCONCEPT

SUMMARY

c2 < a2 + b2

Acutec2 = a2 + b2

Right

c2 > a2 + b2

Obtuse

USE THE CONVERSE OF THE PYTHAGOREAN THEOREM

AB

C

b

ac

A

BC b

ac

AC

B

b

ac

Converse of the Pythagorean Theorem9.3

USE THE CONVERSE OF THE PYTHAGOREAN THEOREM

With c as the longest side, fill in c2 = a2 + b2

Converse of the Pythagorean Theorem9.3

USE THE CONVERSE OF THE PYTHAGOREAN THEOREM

With c as the longest side, fill in c2 = a2 + b2

152 = 122 + 92

225 = 144 + 81

225 = 225

The triangle is a right triangle

Converse of the Pythagorean Theorem9.3

USE THE CONVERSE OF THE PYTHAGOREAN THEOREM

169 149

Not a Right Triangle

180 = 180

Right Triangle

Converse of the Pythagorean Theorem9.3

USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE

Make sure they can form a triangle, then compare c2 to a2 + b2

Converse of the Pythagorean Theorem9.3

USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE

Make sure they can form a triangle, then compare c2 to a2 + b2

Converse of the Pythagorean Theorem9.3

USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE

Make sure they can form a triangle, then compare c2 to a2 + b2

222 565_____9

Compare c2 with a2 + b2

5625_____81

222 ba_____c

Substitute

Multiply

c2 = a2 + b28181

Since c2 = a2 + b2, the triangle is a right triangle

Converse of the Pythagorean Theorem9.3

USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE

12, 16, 20

400 = 400

The triangle is a right triangle

1681 > 1664

The triangle is obtuse