1. What is a right triangle? It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse. leg hypotenuse right angle

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5. Find the length of the hypotenuse if 1. a = 12 and b = 16. 12 2 + 16 2 = c 2 144 + 256 = c 2 400 = c 2 Take the square root of both sides. 20 = c

6. 5 2 + 7 2 = c 2 25 + 49 = c 2 74 = c 2 Take the square root of both sides. 8.60 = c Find the length of the hypotenuse if 2. a = 5 and b = 7.

7. Find the length of the leg, to the nearest hundredth, if 3. a = 4 and c = 10. 4 2 + b 2 = 10 2 16 + b 2 = 100 Solve for b. 16 - 16 + b 2 = 100 - 16 b 2 = 84 b = 9.17

8. Find the length of the missing side given a = 4 and c = 5 1.1 2.3 3.6.4 4.9

9. What are Pythagorean Triples? Three integers that make the equation a 2 + b 2 = c 2 true are called Pythagorean Triples. The numbers 3, 4 and 5 are a very famous Pythagorean Triple. a 2 + b 2 = c 2 3 2 + 4 2 = 5 2 9 + 16 = 25 5, 12, 13 Another common triple

10. Practice: Are they Pythagorean Triples? 1) yes or no?2) yes or no?

11. 9 + 64 = 73 73 = 73 Since this is true, the triangle is a right triangle!! If it was not true, it would not be a right triangle. Sides:, 3, and 8 3 2 + 8 2 = ( ) 2

12. Pythagorean Inequality Theorem

13. a & b are the legs c is the hypotenuse a 2 + b 2 = c 2 c a b Pythagorean Inequalities: c 2 > a 2 + b 2 - - - Triangle is obtuse c 2 < a 2 + b 2 - - - Triangle is acute

14. Pythagorean Inequalities The following triples represent the side lengths of a triangle. Determine whether the triangle is right, acute or obtuse. 1.5, 9, 12 2.7, 24, 26 3.13, 15, 17 4.3, 4, 5 5.25, 25, 30 Obtuse Acute Right Acute