Chapter 5.4, Problem 44E

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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.

**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

Now we have to prove

By forming a table,

1 | Given | |

2 | AN altitude is a segment from a vertex and perpendicular the opposite side |

Sect-5.1 P-1ESect-5.1 P-2ESect-5.1 P-3ESect-5.1 P-4ESect-5.1 P-5ESect-5.1 P-6ESect-5.1 P-7ESect-5.1 P-8ESect-5.1 P-9ESect-5.1 P-10E

Sect-5.1 P-11ESect-5.1 P-12ESect-5.1 P-13ESect-5.1 P-14ESect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-29ESect-5.1 P-30ESect-5.1 P-31ESect-5.1 P-32ESect-5.1 P-33ESect-5.1 P-34ESect-5.1 P-35ESect-5.1 P-36ESect-5.1 P-37ESect-5.1 P-38ESect-5.1 P-39ESect-5.1 P-40ESect-5.1 P-41ESect-5.2 P-1ESect-5.2 P-2ESect-5.2 P-3ESect-5.2 P-4ESect-5.2 P-5ESect-5.2 P-6ESect-5.2 P-7ESect-5.2 P-8ESect-5.2 P-9ESect-5.2 P-10ESect-5.2 P-11ESect-5.2 P-12ESect-5.2 P-13ESect-5.2 P-14ESect-5.2 P-15ESect-5.2 P-16ESect-5.2 P-17ESect-5.2 P-18ESect-5.2 P-19ESect-5.2 P-20ESect-5.2 P-21ESect-5.2 P-22ESect-5.2 P-23ESect-5.2 P-24ESect-5.2 P-25ESect-5.2 P-26ESect-5.2 P-27ESect-5.2 P-28ESect-5.2 P-29ESect-5.2 P-30ESect-5.2 P-31ESect-5.2 P-32ESect-5.2 P-33ESect-5.2 P-34ESect-5.2 P-35ESect-5.2 P-36ESect-5.2 P-37ESect-5.2 P-38ESect-5.2 P-39ESect-5.2 P-40ESect-5.3 P-1ESect-5.3 P-2ESect-5.3 P-3ESect-5.3 P-4ESect-5.3 P-5ESect-5.3 P-6ESect-5.3 P-7ESect-5.3 P-8ESect-5.3 P-9ESect-5.3 P-10ESect-5.3 P-11ESect-5.3 P-12ESect-5.3 P-13ESect-5.3 P-14ESect-5.3 P-15ESect-5.3 P-16ESect-5.3 P-17ESect-5.3 P-18ESect-5.3 P-19ESect-5.3 P-20ESect-5.3 P-21ESect-5.3 P-22ESect-5.3 P-23ESect-5.3 P-24ESect-5.3 P-25ESect-5.3 P-26ESect-5.3 P-27ESect-5.3 P-28ESect-5.3 P-29ESect-5.3 P-30ESect-5.3 P-31ESect-5.3 P-32ESect-5.3 P-33ESect-5.3 P-34ESect-5.3 P-35ESect-5.3 P-36ESect-5.3 P-37ESect-5.3 P-38ESect-5.3 P-39ESect-5.3 P-40ESect-5.3 P-41ESect-5.3 P-42ESect-5.3 P-43ESect-5.4 P-1ESect-5.4 P-2ESect-5.4 P-3ESect-5.4 P-4ESect-5.4 P-5ESect-5.4 P-6ESect-5.4 P-7ESect-5.4 P-8ESect-5.4 P-9ESect-5.4 P-10ESect-5.4 P-11ESect-5.4 P-12ESect-5.4 P-13ESect-5.4 P-14ESect-5.4 P-15ESect-5.4 P-16ESect-5.4 P-17ESect-5.4 P-18ESect-5.4 P-19ESect-5.4 P-20ESect-5.4 P-21ESect-5.4 P-22ESect-5.4 P-23ESect-5.4 P-24ESect-5.4 P-25ESect-5.4 P-26ESect-5.4 P-27ESect-5.4 P-28ESect-5.4 P-29ESect-5.4 P-30ESect-5.4 P-31ESect-5.4 P-32ESect-5.4 P-33ESect-5.4 P-34ESect-5.4 P-35ESect-5.4 P-36ESect-5.4 P-37ESect-5.4 P-38ESect-5.4 P-39ESect-5.4 P-40ESect-5.4 P-41ESect-5.4 P-42ESect-5.4 P-43ESect-5.4 P-44ESect-5.4 P-45ESect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.5 P-25ESect-5.5 P-26ESect-5.5 P-27ESect-5.5 P-28ESect-5.5 P-29ESect-5.5 P-30ESect-5.5 P-31ESect-5.5 P-32ESect-5.5 P-33ESect-5.5 P-34ESect-5.5 P-35ESect-5.5 P-36ESect-5.5 P-37ESect-5.5 P-38ESect-5.6 P-1ESect-5.6 P-2ESect-5.6 P-3ESect-5.6 P-4ESect-5.6 P-5ESect-5.6 P-6ESect-5.6 P-7ESect-5.6 P-8ESect-5.6 P-9ESect-5.6 P-10ESect-5.6 P-11ESect-5.6 P-12ESect-5.6 P-13ESect-5.6 P-14ESect-5.6 P-15ESect-5.6 P-16ESect-5.6 P-17ESect-5.6 P-18ESect-5.6 P-19ESect-5.6 P-20ESect-5.6 P-21ESect-5.6 P-22ESect-5.6 P-23ESect-5.6 P-24ESect-5.6 P-25ESect-5.6 P-26ESect-5.6 P-27ESect-5.6 P-28ESect-5.6 P-29ESect-5.6 P-30ESect-5.6 P-31ESect-5.6 P-32ESect-5.6 P-33ESect-5.6 P-34ESect-5.6 P-35ESect-5.6 P-36ESect-5.6 P-37ESect-5.6 P-38ESect-5.6 P-39ESect-5.6 P-40ESect-5.CR P-1CRSect-5.CR P-2CRSect-5.CR P-3CRSect-5.CR P-4CRSect-5.CR P-5CRSect-5.CR P-6CRSect-5.CR P-7CRSect-5.CR P-8CRSect-5.CR P-9CRSect-5.CR P-10CRSect-5.CR P-11CRSect-5.CR P-12CRSect-5.CR P-13CRSect-5.CR P-14CRSect-5.CR P-15CRSect-5.CR P-16CRSect-5.CR P-17CRSect-5.CR P-18CRSect-5.CR P-19CRSect-5.CR P-20CRSect-5.CR P-21CRSect-5.CR P-22CRSect-5.CR P-23CRSect-5.CR P-24CRSect-5.CR P-25CRSect-5.CR P-26CRSect-5.CR P-27CRSect-5.CR P-28CRSect-5.CR P-29CRSect-5.CR P-30CRSect-5.CR P-31CRSect-5.CR P-32CRSect-5.CR P-33CRSect-5.CR P-34CRSect-5.CR P-35CRSect-5.CR P-36CRSect-5.CR P-37CRSect-5.CR P-38CRSect-5.CR P-39CRSect-5.CR P-40CRSect-5.CR P-41CRSect-5.CR P-42CRSect-5.CT P-1CTSect-5.CT P-2CTSect-5.CT P-3CTSect-5.CT P-4CTSect-5.CT P-5CTSect-5.CT P-6CTSect-5.CT P-7CTSect-5.CT P-8CTSect-5.CT P-9CTSect-5.CT P-10CTSect-5.CT P-11CTSect-5.CT P-12CTSect-5.CT P-13CTSect-5.CT P-14CTSect-5.CT P-15CTSect-5.CT P-16CTSect-5.CT P-17CT

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