9.1 (old geometry book) Similar Triangles

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Presentation transcript:

9.1 (old geometry book) Similar Triangles 5.4-9.1 HW Quiz: Wednesday Special Triangles Test: FRIDAY!

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

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

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 B A D C

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.

Example 1 cont’d:

Theorem 9.2 In the diagram: In other words: 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: hypotenuse right mean geometric

Theorem 9.3 right 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: hypotenuse geometric mean hypotenuse adjacent

Example 2: Solve for the missing variable:

Homework 9.1 Worksheet