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Math
GeometryElementary Geometry for College Students6th Edition

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

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Chapter
Section
Problem 1E
Problem 2E
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Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Use Figures 5.20 and 5.21 to prove Lemma 5.4.3.

Chapter 5.4, Problem 44E, Use Figures 5.20 and 5.21 to prove Lemma 5.4.3. Lemma 5.4.3 The length of each leg of a right

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.

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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