The Pythagorean Theorem Lesson 3-8 The Pythagorean Theorem Problem of the Day Lesson Presentation Lesson Quizzes

Problem of the Day A side of a square A is 5 times the length of a side of square B. How many times as great is the area of square A than the area of square B?

Vocabulary Pythagorean Theorem leg hypotenuse

This amazing fact is called Years ago, a man named Pythagoras found an amazing fact about triangles… If the triangle had a right angle (90°) ... ... and you made a square on each of the three sides, then ... the biggest square had the exact same area as the other two squares put together! Area = c2 Area = a2 Hypotenuse c a This amazing fact is called "Pythagorean Theorem" b Area = b2

Find the length of the unknown side in the right triangle Use the Pythagorean Theorem The Pythagorean Theorem States that the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Hypotenuse (c) Leg (a) a2 + b2 = c2 Leg (b) EXAMPLE 1 Find the length of the unknown side in the right triangle c = a2 + b2 c 5 12 c = 52 + 122 c = 25 + 144 = 169 = 13

Find the length of the unknown side in the right triangle EXAMPLE 2 Find the length of the unknown side in the right triangle b = c2 - a2 25 8 b b = 252 - 82 b = 625 - 64 b = 561

Two airplanes leave the same airport at the same time Two airplanes leave the same airport at the same time. The first plane flies to a landing strip 80 km south, while the other plane flies to an airport 60 km west. How far apart are the two planes after they land? EXAMPLE 3 c 80 60 c = a2 + b2 c = 602 + 802 c = 3600 + 6400 c = 10000 c = 100

4 Find the length of the unknown side. (–2, 4)‏ (–2, –2)‏ (3, –2)‏ EXAMPLE 4 Find the length of the unknown side. Triangle with coordinates (–2, –2), (–2, 4), and (3, –2)‏ The points form a right triangle. x y (–2, 4)‏ c = a2 + b2 c = 52 + 62 c = 25 + 36 (–2, –2)‏ (3, –2)‏ c = 61

Lesson Quiz Use the figure for Problems 1 and 2. 1. Find the height h of the triangle. 8 m 2. Find the length of side c to the nearest meter. 10 m c h 12 m 3. An escalator is 32 ft tall and 40 ft from a wall. What distance does the escalator carry shoppers? 6 m 9 m 2624 ≈ 51 ft

Lesson Quiz for Student Response Systems 1. Identify the height of the triangle. A. 14 m B. 15 m C. 16 m D. 17 m 10 10

Lesson Quiz for Student Response Systems 2. Identify the length of side c to the nearest meter. A. 9 m B. 10 m C. 11 m D. 12 m 11 11

Lesson Quiz for Student Response Systems 3. The height of a tower is 30 ft. It casts a shadow of 36 ft on the ground. What is the distance between the tip of the tower to the corresponding tip of its shadow? A. B. C. D. 12 12