In the previous section, an animation was used to create three similar right triangles from drawing the altitude, h, from the right angle to the hypotenuse of a right triangle. The two segments of the hypotenuse created on either side of the point of intersection are represented by r and s.

Are these two triangles similar? Why?

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In any right triangle, the acute angles are complementary. Also, complements of the same angle are congruent.

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AA similarity verifies that the triangles are similar.

Write a proportion to show two equal ratios of corresponding sides for these two similar triangles.

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r h = h s

How does your proportion relate to your original figure?

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r and s represent the hypotenuse segments, and h represents the length of the altitude.

In the proportion, h is the cross product of both ratios. When one cross product contains the same quantity, it is said to be the geometric mean of the other two quantities. This proportion can be read, “h is the geometric mean of r and s.”