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Similarity in Right Triangles

Similarity in Right Triangles. Geometry CP2 (Holt 8-1) K. Santos. Parts of a Right Triangle. A B C Hypotenuse—side opposite the right angle Legs—sides that form the right angle and . Altitude to the Hypotenuse. X

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Similarity in Right Triangles

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  1. Similarity in Right Triangles Geometry CP2 (Holt 8-1) K. Santos

  2. Parts of a Right Triangle A B C Hypotenuse—side opposite the right angle Legs—sides that form the right angle and

  3. Altitude to the Hypotenuse X P Y Z Altitude—is the segment that is starts at a vertex and is perpendicular a side (in this case the hypotenuse)

  4. Theorem(8-1-1) The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle. A D CBD B C

  5. Geometric Mean The geometric mean of a and b is the positive number x such that: = . = ab x =

  6. Geometric Mean Example Find the geometric mean between 4 and 12. = abuse a = 4 and b = 12 = 4(12) = 48 x = x = 4

  7. Corollary (8-1-1) = x = so = xy y h

  8. Example Solve for x. x 15 5 = 15(5) = 75 x = x = 5

  9. Corollary (8-1-2) = = so = xc = so = yc c x a y b

  10. Example Find x. 4 x 21 Find the entire hypotenuse: 21+ 4 = 25 = 25(4) = 100 x = x = 10

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