1. Bell Ringer What is the measurement of the missing angles? 38˚ b a c d a = 142°, supplementary b = 142°, alternate interior angle c = 38°, corresponding or supplementary d = 52°, triangles = 180°

2. Classwork/Homework

3. REVIEW FROM FRIDAY! Pythagorean Theorem

4. Right Triangles Hypotenuse – Longest side is the hypotenuse, side c (opposite the 90 o angle) The other two sides are the legs, sides a and b Hypotenuse (c) Leg (a) Leg (b) It doesn’t matter which leg is “a” or “b”. The hypotenuse is always side c!

5. The Pythagorean Theorem In a RIGHT Triangle, if sides “a” and “b” are the legs and side “c” is the hypotenuse, then a 2 + b 2 = c 2 a b c

6. The Pythagorean Theorem Find the missing side. a 15 17 a 2 + b 2 = c 2 a 2 + 15 2 = 17 2 a 2 + 225 = 289 a 2 = 64 a = √64 = 8

7. The Pythagorean Theorem Chris’ window is 12 feet high. If he placed his ladder 9 feet away from the base of the house, how long is the ladder? a 2 + b 2 = c 2 9 2 + 12 2 = c 2 81 + 144 = c 2 225 = c 2 √225 = c 15 feet = c Ladder = c Base = 9 ft Window = 12 ft

8. The Pythagorean Theorem Three points are located on a coordinate plane. How long is the diagonal formed by the three points? a 9 8 a 2 + b 2 = c 2 8 2 + 9 2 = c 2 64 + 81 = c 2 145 = c 2 c = √145 = 12.04 b c c We could have used the distance formula to solve this!

9. PPF 502 - RECOGNIZE PYTHAGOREAN TRIPLES* Pythagorean Triples

10. Pythagorean Triples are three positive whole numbers that fit the rule “ a 2 + b 2 = c 2”. The most famous triple is 3, 4, 5. This means that the legs are 3 & 4, while the hypotenuse is 5. The hypotenuse is the longest side. 5 3 4 a 2 + b 2 = c 2 3 2 + 4 2 = 5 2 9 + 16 = 25 25 = 25 This is true, so 3, 4, 5 is a triple!

11. Pythagorean Triples Any multiple of a Pythagorean Triple is also true. So, any multiple of 3, 4, 5 is also a triple. 6, 8, 10 (multiply by 2) is a triple. 10 6 8 a 2 + b 2 = c 2 6 2 + 8 2 = 10 2 36 + 64 = 100 100 = 100 This is true, so 6, 8, 10 is a triple!

12. Pythagorean Triples Determine whether a triangle with lengths 7, 11, and 12 form a right triangle. (The hypotenuse is always the longest length.) 12 7 11 a 2 + b 2 = c 2 7 2 + 11 2 = 12 2 49 + 121 = 144 170 = 144 This is NOT true, so this is not a right triangle!

13. Pythagorean Triples Determine whether a triangle with lengths 12, 16, and 20 form a right triangle. (The hypotenuse is always the longest length.) 20 12 16 a 2 + b 2 = c 2 12 2 + 16 2 = 20 2 144 + 256 = 400 400 = 400 This IS true, so this is a right triangle! This is also a multiple of 3, 4, 5 triple!