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9.1 Similar Triangles

9.1 Similar Triangles. Similar Triangles. In order for two triangles to be similar: Their angles must be _____________ Their ___________ sides must be ____________. congruent. corresponding. proportional. Geometric Mean.

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9.1 Similar Triangles

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  1. 9.1 Similar Triangles

  2. Similar Triangles In order for two triangles to be similar: • Their angles must be _____________ • Their ___________ sides must be ____________ congruent corresponding proportional

  3. Geometric Mean • The Altitude of a triangle is the _____________ segment from a _____________ to the ____________ side. • The Altitude is called the Geometric Mean. Draw a picture: perpendicular vertex opposite B D C A

  4. B D C A Theorem 9.1 altitude • If the ______________ is drawn to the hypotenuse of a ___________ triangle, then the two triangles formed are ____________ to the ____________ triangle and to each other. • Draw a picture and write the three SIMILARITY STATEMENTS: right similar original

  5. Example 1: • A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. a) Identify the similar triangles in the diagram. b) Find the height of h.

  6. Example 1 cont’d:

  7. Theorem 9.2 hypotenuse right • In a right triangle, the altitude from the _____________ angle to the ____________ divides the hypotenuse into two segments. The length of the altitude is the ___________ _____________ of the lengths of the two segments. • In the diagram: • In other words: mean geometric

  8. Theorem 9.3 right hypotenuse • In a right triangle, the altitude from the ___________ angle to the _____________ divides the hypotenuse into two segments. The length of each leg of the right triangle is the _________________ _________ of the lengths of the ____________ and the segment of the hypotenuse that is _____________ to the leg. • In the diagram: • In other words: geometric mean hypotenuse adjacent

  9. Example 2: • Solve for the missing variable:

  10. Independent Classwork Let’s find b, c, and d. Then finish the Practice Problems from Yesterday. (Worksheet)

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