   Chapter 5.4, Problem 44E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

Use Figures 5.20 and 5.21 to prove Lemma 5.4.3. Lemma 5.4.3The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

To determine

To prove :

The lemma 5.4.3 “The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg”.

Explanation

Given figures 5.19 and 5.20

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

Now we have to prove ABAC=ACAD.

By forming a table,

 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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