c = 10 c = 5

Chapter 9 Right 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

In a triangle, if c2 = a2 + b2, then the triangle is a right triangle USE THE CONVERSE OF THE PYTHAGOREAN THEOREM THEOREM THEOREM 9.5 Converse of the Pythagorean Theorem In a triangle, if c2 = a2 + b2, then the triangle is a right triangle A B C b a c ABC is a right Triangle  c 2 = a 2 + b 2

In a triangle, if c2 < a2 + b2, then the triangle is acute USE THE CONVERSE OF THE PYTHAGOREAN THEOREM THEOREM In a triangle, if c2 < a2 + b2, then the triangle is acute A B C b a c ABC is acute c 2 < a 2 + b 2

In a triangle, if c2 > a2 + b2, then the triangle is obtuse USE THE CONVERSE OF THE PYTHAGOREAN THEOREM THEOREM In a triangle, if c2 > a2 + b2, then the triangle is obtuse A C B b a c ABC is obtuse c 2 > a 2 + b 2

A B C A B C A C B USE THE CONVERSE OF THE PYTHAGOREAN THEOREM CONCEPT SUMMARY A B C A B C A C B b a c b a c b a c c2 < a2 + b2  Acute c2 = a2 + b2  Right c2 > a2 + b2 Obtuse

With c as the longest side, fill in c2 = a2 + b2 USE THE CONVERSE OF THE PYTHAGOREAN THEOREM With c as the longest side, fill in c2 = a2 + b2

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

169  149 180 = 180 Right Triangle Not a Right Triangle USE THE CONVERSE OF THE PYTHAGOREAN THEOREM 169  149 Not a Right Triangle 180 = 180 Right Triangle

Make sure they can form a triangle, then compare c2 to a2 + b2 USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c2 to a2 + b2

Make sure they can form a triangle, then compare c2 to a2 + b2 USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c2 to a2 + b2

Since c2 = a2 + b2, the triangle is a right triangle USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c2 to a2 + b2 Compare c2 with a2 + b2 Substitute Multiply c2 = a2 + b2 Since c2 = a2 + b2, the triangle is a right triangle

Closure Question 12, 16, 20 400 = 400 1681 > 1664 The triangle is a right triangle 1681 > 1664 The triangle is obtuse