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8-1 Vocabulary Geometric mean
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8-1 Similarity in Right Triangles
Geometry
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8-1-1 Theorem The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other & to the original triangle. B D C A
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Example 1 Write a similarity statement comparing the 3 triangles. Z
V U W
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Geometric mean The geometric mean of two positive numbers is the positive square root of their product.
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Example 2 Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. a.) 4 and 25 b.) 5 and 30
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Geometric Mean Corollaries
8-1-2 Corollary The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.
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Geometric Mean Corollaries
8-1-3 Corollary The length of a leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse & the segment of the hypotenuse adjacent to the leg.
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Example 3 Find x, y & z. x y 6 z
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Ex. 4 To estimate the height of a Douglas fir, Jan positions herself so that her lines of sight to the top & bottom of the tree form a 90° angle. Her eyes are about 1.6 m above the ground, and she is standing 7.8 m from the tree. What is the height of the tree to the nearest meter?
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