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Pythagorean Theorem and its converse

Pythagorean Theorem and its converse. Section 8-1. Pythagorean Theorem. In a right triangle the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. a 2 + b 2 = c 2. c. Hypotenuse. a. Leg. b. Leg. Example 1.

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Pythagorean Theorem and its converse

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  1. Pythagorean Theorem and its converse Section 8-1

  2. Pythagorean Theorem In a right triangle the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. a2 + b2 = c2 c Hypotenuse a Leg b Leg

  3. Example 1 In the following figure if A = 8 and B = 6, Find C. C A B Lesson 7-2: The Pythagorean Theorem

  4. 2. A=8, B= 15, Find C 3. A=7, B= 24, Find C Pythagorean Theorem : Examples 2 and 3 C = 17 C = 25 C A B Lesson 7-2: The Pythagorean Theorem

  5. Solve for x 4. x 3 5 5. x 4 6

  6. Word problems ex. 6 • The foot of a ladder is 6 feet from a wall. If the top of the ladder rests 8 feet up a wall, how long is the ladder?

  7. Example 7 Randy made a ramp for his dog to get into his truck. The ramp is 6 ft long and the bed of the truck is 3ft above the ground. Approximately how far from the back of the truck does the ramp touch the ground?

  8. Example 8 • Donna’s TV screen is 20 inches long. If the diagonal measures 25 inches, what is the width of the tv screen?

  9. Example 9 • Town A is 9 miles from town B, and 12 miles from town C. A road connects towns B and C directly. Find the length of this road. Angle B is the right angle.

  10. Converse of the Pythagorean theorem If the sum of the square of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. If a2 + b2 = c2, then ∆ABC is a right triangle. B c a A C b

  11. Tell whether it is a right triangle: 14 10. 22 11. 9 26 15

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