Lesson 8-7 The Pythagorean Theorem

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Presentation transcript:

Lesson 8-7 The Pythagorean Theorem Thee’uh-rem (named after Pythagoras)

Building squares on right angles Copy the image from the school text book and paste it on the slide or use sketchpad to create the same image in the book 2

Pythagorean theorem In any right triangle, the sum of the squares of the lengths a and b of the legs is equal to the square of the length c of the hypotenuse. Baseball diamond Height of a building Ramp of a moving truck Measurement of TV Two friends meeting at a particular destination 3

The Pythagorean Theorem LESSON 8-7 Additional Examples Find the length of the hypotenuse. c2 = a2 + b2 Pythagorean Theorem c2 = 212 + 202 Substitute. c2 = 441 + 400 Simplify. c2 = 841 Take the square root of each side. c2 = 841 c = 29 The length of the hypotenuse is 29 in. 8-7

The Pythagorean Theorem LESSON 8-7 Additional Examples Find the missing leg of the triangle. a2 + b2 = c2 Pythagorean Theorem a2 + 152 = 252 Substitute. a2 + 225 = 625 Simplify. a2 + 225 – 225 = 625 – 225 Subtract 225 from both sides. a2 = 400 Simplify. a = 20 Take the square root of each side. a2 = 400 The length of the leg is 20 ft. 8-7

8.7: Applying the Pythagorean theorem 6

Objective We use Pythagorean theorem to solve real-world situations Sometimes, a triangle is not obvious but you can visualize the sides of a triangle and then draw a picture Now, let’s work on a word problem.

The Pythagorean Theorem LESSON 8-7 Additional Examples A ladder, placed 4 ft from a wall, touches the wall 11.3 ft above the ground. What is the approximate length of the ladder? Draw a diagram to illustrate the problem. c2 = a2 + b2 Use the Pythagorean Theorem. c2 = 42 + 11.32 Substitute. c2 = 143.69 c2 = 16 + 127.69 Square 4 and 11.3. Add. Use a calculator. Take the square root of each side. c = 11.98708 c2 = 143.69 The length of the ladder is about 12 ft. 8-7

Homework Lesson 8-7 pp. 407-408 #s 1-10, 15-18, 22-24 (Can use a calculator if c2 is not a perfect square) Complete Activity Lab if needed.