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1. How can you use similar triangles to find the height of the flag pole in front of the library?

§ 14.1. 1. How can you use similar triangles to find the height of the flag pole in front of the library?. h. l 1. x. l 2. 2. How can you use similar triangles to find the diameter of the earth? . Research Eratosthenes.

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1. How can you use similar triangles to find the height of the flag pole in front of the library?

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  1. § 14.1 1. How can you use similar triangles to find the height of the flag pole in front of the library? h l 1 x l 2

  2. 2. How can you use similar triangles to find the diameter of the earth? Research Eratosthenes.

  3. 3. Find the relationship between the areas of two similar triangles. kh h b kb Area = ½ bh Area = ½ kbkh • If the sides have a ratio of k then the areas have a ratio of k 2.

  4. 4. Prove that if a line parallel to one side of a triangle intersects the other two sides, then it cuts off a similar triangle. C D E Given: AB  DE. Prove: ∆ABC ~ ∆DEC B A

  5. A D B E C F 5. Prove SSS similarity. Given: Prove: ∆ABC ~ ∆DEF F’ E’

  6. 6. Prove that the altitude to the hypotenuse separates the triangle into two triangles which are similar to each other and to the original triangle. Because of the right triangle and a common angle in each of the triangles it is easy to show the triangles similar by AA or AAA.

  7. 7. Find the length of the altitude to the hypotenuse of a right triangle with legs of 15 and 20. Use the Pythagorean Theorem to find the hypotenuse of 25. then And you know a, b and c, so

  8. 8. A method used by carpenters to divide a board into equal parts is to use the vertical studding of a building as parallel lines, and to place the board to be divided transversely across them. Why does this work? Notice all of the similar triangles.

  9. 9. In rectangle ABCD construct the diagonal AC. Construct the altitude from D to AC meeting AC at E. Prove that ∆CDE ~ ∆ABC. C D E A B Because of the right triangle and a common angle in each of the triangles it is easy to show the triangles similar by AA or AAA.

  10. C C D H A B 10. In the figure below ∆ABC ~ ∆DAB. Prove that AB is the geometric mean between AD and BC. D H A B Because ∆ABC ~ ∆DAB we have the following proportions - And the first proportion gives us AB as the geometric mean between AD and BC>

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