7.3 Use Similar Right Triangles

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Presentation transcript:

7.3 Use Similar Right Triangles Before: You identified altitudes of a triangle. Now: You will use properties of the altitude in right triangles. Why: So you can determine the height of an object.

Theorem 7.5 If an altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

Identify the three similar triangles in the diagram

Your turn Identify the three similar right triangles in the given diagrams.

Find the length of the altitude Step 1: Identify the three similar triangles created by the altitude and sketch them. Step 2: Write a proportion to find the value of h. In similar figures corresponding sides are proportional

Identify the similar triangles. Then find the value of x. Sketch the 3 similar triangles. Write a proportion to find x. x=12/5 X=60/13

Geometric Mean

Geometric Mean (Altitude) Theorem The length of the altitude is the geometric mean of the lengths of the hypotenuse segments

Geometric Mean (Leg) Theorem The length of each leg is the geometric mean of the lengths of the hypotenuse and the adjacent hypotenuse segment.

Proportions Involving Geometric Means in Right ∆ABC Similar Triangles Connections to geometric mean What you would be given in each situation Label a, b, and x http://www.youtube.com/watch?v=PXBFDBmBP0I

Find the value of y Geometric Mean Formulas Label the parts and use the formula to create a proportion. Solve for the variable. Triangle Similarity Identify the 3 similar triangles and sketch them. Write a proportion

Your Turn Find the value of the variable.

Assignment Pg 453 # 1-9 odd, 13-23 odd, 29 Quiz 7.1-7.3 next class period