Lesson 83 The Pythagorean Theorem Do Now Find

Lesson 83: The Pythagorean Theorem Do Now: Find the missing side of the right triangle below. Show all work! 39 x 15 a² + b² = c² 15² + x² = 39² 225 + x² = 1521 - 225 x² = 1296 x = 36

Text Page 461 1)5 3 2)3 30 3)3 15 4)(2 7)/7 5)(5 2)/2 6)2 6 7) x = 9 8) x = 7. 5 9) x = 32 10) x = 9. 2 11) x = 2 12) x = 17

Right Triangle Notes po leg Reminder: hy Right Angle ten leg us e

A Pythagorean Triple is a set of three nonzero whole numbers or positive integers that satisfy the Pythagorean Theorem.

a² + b² = c² 15² + x² = 25² 225 + x² = 625 – 225 x² = 400 x = 20

a² + b² = c² 8. 5² + 15. 1² = x² 72. 25 + 228. 01 = x² 300. 26 = x² 17. 3 x *Round answer to the nearest tenth

This theorem is used to prove a triangle is a right triangle.

a² + b² = c² 8² + (4 5)² = 12² 64 + 80 = 144 By the Converse of the Pythagorean Theorem, a right triangle exists. a² + b² = c² 9² + (2 30)² = 14² 81 + 120 = 196 201 = 196 By the Converse of the Pythagorean Theorem, a right triangle DOES NOT exist.

This theorem can be applied to any type of triangle!

1. Use the Triangle Inequality Theorem to determine if a triangle exists. 2. Compare the square of the length of the longest side with the sum of the squares of the lengths of the other 2 sides.

HW # 81: (DUE Tuesday 1/22) Big Ideas pp. 468 - 470 #1, 2, 6 - 30 even Make index cards for today’s 3 theorems Midterm Exam Tomorrow Bring Pens and Pencils!