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Geometry worksheet in which students name acute angles, hypotenuses, and legs in right triangles with altitudes to the hypotenuse, and complete the proof of the related geometric mean theorem.

Activity 3.8​

Assignment 3.9

​Assignment 6.21

​Similar Right Triangles and the Geometric Mean

 
Objective
Develop and apply a geometric mean theorem for right triangles with an altitude to the hypotenuse.
 
 
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Geometry worksheet in which students name hypotenuses, legs, and geometric means in right triangles with altitudes to the hypotenuse, set up and solve proportions using a geometric mean theorem.

About Geometry Worksheet Assignment 6.21:     

 

Assignment 6.21 is a development and application of the geometric mean theorem for similar right triangles determined by the altitude to the hypotenuse in a right triangle.

 

Prerequisite Skills:  Identify right angles, acute angles, legs and hypotenuses in right triangles (Assignment 3.13).  Solve proportions (Assignment 6.2).

 

Theorem:  In a right triangle with an altitude dividing the hypotenuse into two segments, the length of each leg is the geometric mean of the lengths of the

                       hypotenuse and the segment of the hypotenuse with a common endpoint with the leg.

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