Pythagorean Theorem and It’s Converse You have not lived a perfect day, unless you've done something for someone who will never be able to repay you. -- Ruth Smeltzer Pythagorean Theorem and It’s Converse Chapter 8 Section 2 Learning Goal: Learn/Apply the Pythagorean Th. and it’s converse

There are at least 80 different ways to prove the Pythagorean theorem 9 16 25 There are at least 80 different ways to prove the Pythagorean theorem Link to AgileMinds #13, Patty Paper Proof, 1-8

Pythagorean Theorem Find the missing measures 12.7 √27

Converse of the Pythagorean Th. Determine whether the sides of these triangles could form a right triangle 9, 12, 15 4√3, 4, 8 5, 8, 9 yes yes no

Coordinate Geometry Verify that ∆ABC is a right ∆

Pythagorean Triple A Pythagorean Triple is three whole numbers that satisfy the equation a2 + b2 = c2 . (Remember our answers from before) 9, 12, 15 4√3, 4, 8 5, 8, 9 Are each of these 3 numbers a Pythagorean Triple? rt. ∆ Yes rt. ∆ No not a rt. ∆ No The most common Pythagorean Triple = 3-4-5

Pythagorean Triple Determine whether 30, 40, and 50 are the sides of a right triangle. Then state whether they form a Pythagorean triple. Yes, and Yes

Closer Look What do we know about a triangle with sides: 6, 8, 10? 6, 8, 12? 6, 8, 9? 10 6 Right Triangle 36 + 64 = 100 8 6 8 12 Obtuse Triangle 36 + 64 < 144 6 8 9 Acute Triangle 36 + 64 > 81

Converse of Pythagorean Th. a2 + b2 = c2  Right Angle c2 > a2 + b2  c2 < a2 + b2  Obtuse Angle Acute Angle What about . . . 1. 2, 3, 4 2. 7, 8, 5√3 > 42 32 + 22 Obtuse ∆ < 5√3 72 + 82 Acute ∆

Homework Pythagorean Theorem and Its Converse Worksheet