1 / 9

Lesson 8-7 The Pythagorean Theorem

Lesson 8-7 The Pythagorean Theorem. The Py-tha’-go-rean Thee’uh-rem (named after Pythagoras). Building squares on right angles. 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.

lani
Download Presentation

Lesson 8-7 The Pythagorean Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lesson 8-7The Pythagorean Theorem The Py-tha’-go-rean Thee’uh-rem (named after Pythagoras)

  2. Building squares on right angles

  3. 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.

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

  5. 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. a2 = 400 Take the square root of each side. a = 20 The Pythagorean Theorem LESSON 8-7 Additional Examples Find the missing leg of the triangle. The length of the leg is 20 ft. 8-7

  6. 8.7: Applying the Pythagorean theorem

  7. 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.

  8. Draw a diagram to illustrate the problem. Use the Pythagorean Theorem. Use the Pythagorean Theorem. c2 = a2 + b2 c2 = 42 + 11.32 Substitute. c2 = 16 + 127.69 Square 4 and 11.3. c2 = 143.69 Add. Take the square root of each side. c2 = 143.69 c = 11.98708 Use a calculator. 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? The length of the ladder is about 12 ft. 8-7

  9. 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.

More Related