Chapter 5.4, Problem 43E

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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

Now we have to prove

**Calculation:**

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-5.1 P-42ESect-5.1 P-43ESect-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-5.5 P-39ESect-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-5.6 P-41ESect-5.6 P-42ESect-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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