   Chapter 5.3, Problem 37E 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 the result of Exercise 13 to do the following problem. In ▱ M N P Q , Q P = 12 and Q M = 9 . The length of altitude Q R ¯ (to side M N ¯ ) is 6. Find the length of altitude Q S ¯ from Q to P N ¯ . To determine

To find:

The length of altitude QS¯ from Q to PN¯.

Explanation

Given:

Given: MNPQ, QP=12, QM=9, and the length of altitude QR¯ (to side MN¯) is 6.

Definition:

AA:

If the two angles of one triangle are congruent to the two angles of another triangle, then the triangles are similar.

CSSTP:

Corresponding sides of similar triangles are proportional.

Description:

Given that MNPQ,.

From the given figure, it is observed that there are two altitudes QR¯ and QS¯.

An altitude is a line segment through a vertex and perpendicular to a line of a base.

That is, QR¯MN¯ and QS¯PN¯.

It is known that two lines are perpendicular, they form right angles. That is, QRM and QSP are right triangles.

Since all right angles are congruent, QRMQSP.

The opposite angles of are congruent. So that RS.

The above mentioned AA definition, the two triangles QRM and QSP are similar since the two angles of one triangle are congruent to two angles of another triangle

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