9.1 Pythagorean Theorem

What We Will Learn Use Pythagorean Thm Use converse of Pythagorean Thm Classify Triangles

Needed Vocab Pythagorean triple: set of three positive integers a, b, and c that satisfy the equation 𝑐 2 = 𝑎 2 + 𝑏 2

Exs. 1/2/3 Using Pythagorean Thm. Find x C is ALWAYS opposite the right angle and is the longest side, a and b don’t matter on order 𝑎 2 + 𝑏 2 = 𝑐 2 5 2 + 12 2 = 𝑥 2 25+144= 𝑥 2 169= 𝑥 2 169 = 𝑥 2 13=𝑥

Exs. 1/2/3 Continued Find x 𝑥 2 + 7 2 = 14 2 𝑥 2 +49=196 −49 −49 −49 −49 𝑥 2 =147 𝑥 2 = 147 𝑥= 49 ∗ 3 𝑥=7 3

Ex. 4 Converse of Pythagorean Thm Is it a right triangle? Remember c is ALWAYS opposite the right angle and longest side 7 2 + 8 2 = 113 2 49+64=113 113=113 Yes

Your Practice Is it a right triangle? 15 2 + 36 2 = 4 95 2 15 2 + 36 2 = 4 95 2 15 2 + 36 2 = 4 2 ∗ 95 2 225+1296=16∗95 1521=1520 no

Ex. 5 Classifying Triangles Key Concept: If 𝑎 2 + 𝑏 2 = 𝑐 2 , then it is a right triangle If 𝑎 2 + 𝑏 2 > 𝑐 2 , then it is an acute triangle If 𝑎 2 + 𝑏 2 < 𝑐 2 , then it is an obtuse triangle Verify that segments make a triangle first Any two segments must add up to be longer than third side Then plug into Pythagorean Thm to classify

Ex. 5 Classify Verify that segments with lengths of 4.3 feet, 5.2 feet, and 6.1 feet form a triangle. Then classify the triangle. 4.3+5.2>6.1, 4.3+6.1>5.2, 5.2+6.1>4.3 9.5>6.1 10.4>5.2 11.3>4.3 4.3 2 + 5.2 2 = 6.1 2 18.49+27.04=37.21 45.53>37.21 acute