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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Use Figure 5.19 to prove Theorem 5.4.2.

Theorem 5.4.2

The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

To determine

To proof :

The theorem 5.4.2, “The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse”.

Explanation

Given:

From the figure ΔABC, with right ACB; CD¯AB¯

Now we have to prove ADCD=CDDB.

Calculation:

1 ΔABC with right ACBCD¯AB¯ Given
2 CD¯ is an altitude to AB¯ AN altitude is a segment from a vertex and perpendicular the opposite side

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