1. Bell Ringer What is the measurement of the missing angles? 65˚ b a cd A triangle sits in between two parallel lines. The sides of the triangle form two transversals. a = 50° b = 65° c = 65° d = 115°

2. Classwork/Homework

3. PPF 502 - RECOGNIZE PYTHAGOREAN TRIPLES* PPF 602 - USE THE PYTHAGOREAN THEOREM Pythagorean Theorem

4. Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as a means to understand the natural world First to teach that the earth was a sphere that revolves around the sun

5. Applications The Pythagorean theorem has many uses in other fields (such as the arts), as well as practical applications. The theorem is invaluable when computing distances between two points, such as in navigation and land surveying. Another important application is in the design of ramps. Ramp designs for handicap-accessible sites and for skateboard parks are very much in demand.

6. 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 Pythagoras developed a formula for finding the length of the sides of any RIGHT triangle Hypotenuse (c) Leg (a) Leg (b) It doesn’t matter which leg is “a” or “b”. The hypotenuse is always side c!

7. 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

8. Finding the Hypotenuse Find the length of the hypotenuse. 12 16 C a 2 + b 2 = c 2 12 2 + 16 2 = c 2 144 + 256 = c 2 400 = c 2 √400 = c 20 = c

9. Finding the Leg Find the length of the missing leg. 29 20 a a 2 + b 2 = c 2 a 2 + 21 2 = 29 2 a 2 + 400 = 841 a 2 = 441 a = √441 a = 21

10. The Ladder Problem A ladder leans against a second- story window of a house. If the ladder is 25 feet long, and the base of the ladder is 7 feet from the house, how high is the window? Ladder = 25 ft Base = 7 ft Window (b) a 2 + b 2 = c 2 7 2 + b 2 = 25 2 49 + b 2 = 625 b 2 = 576 b = √576 b = 24 ft

11. The Baseball Problem The distance between consecutive bases is 90 feet. How far does a catcher have to throw the ball from home plate to second base? The diamond is really a square. If we draw a line from 2 nd base to home, we’ve created two triangles. The distance from 2 nd to home is the hypotenuse and the distance from the bases are the legs!

12. The Baseball Problem a 2 + b 2 = c 2 90 2 + 90 2 = c 2 8100 + 8100 = c 2 16200 = c 2 √16200 = c 127.28 ft = c c

13. We will learn more about recognizing Pythagorean Triples next week! I know you can’t wait! In the meantime, here is some work!