1. Created by Judy L. McDaniel

2. The two sides of a that are to each other are the of the triangle. The side or the side opposite the Angle is the. The lengths can be found using the. a 2 + b 2 = c 2 where and are the legs of the triangle and is always the Hypotenuse. The of the Pythagorean Theorem states that if Hypothetical lengths work in the Pythagorean Theorem, then the lengths form a Triangle. Right Triangle Perpendicular legs longest RightHypotenuse Pythagorean Theorem a b c Converse three Right

3. Problem 1 Find the Length of the Hypotenuse Find the missing length. A. B. 36 x 15 24 7 y a 2 + b 2 = c 2 15 2 + 36 2 = x 2 7 2 + 24 2 = y 2 225 + 1296 = x 2 1521 = x 2 49 + 576 = y 2 39 = x 625 = y 2 25 = y Why not both 39 and –39? Can we have a negative length?

4. Problem 2 Find the Length of a Leg Find the missing length. A. B. 12 13 z 22 10 w a 2 + b 2 = c 2 z 2 + 12 2 = 13 2 10 2 + w 2 = 22 2 z 2 + 144 = 169 100 + w 2 = 484 – 144 = – 144 – 100 = – 100 z 2 = 25 w 2 = 384 z = 5 w ≈ 19.60

5. Problem 3 Identify Right Triangles Decide if the given lengths form a right triangle. A.5in, 8in, 10in B.9m, 40m, 41m C.5cm, 12cm, 17cm D.8ft, 14ft, 17ft a 2 + b 2 = c 2 5 2 + 8 2 = 10 2 5 2 + 12 2 = 17 2 8 2 + 14 2 = 17 2 9 2 + 40 2 = 41 2 Don’t forget the longest side must be “c” 25 + 64 = 100 64 + 196 = 289 81 + 1600 = 1681 25 + 144 = 289 89 ≠ 100 169 ≠ 289 260 ≠ 289 1681 = 1681 NO it is NOT a Rt. TriangleYES it is a Rt. Triangle NO it is NOT a Rt. Triangle Don’t forget the longest side must be “c”

6. 10-1 Pg. 603 #6-28 even, 30-32