   Chapter 3.CR, Problem 18CR ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

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

# Name the longest line segment shown in quadrilateral A B C D . To determine

The longest line segment shown in quadrilateral ABCD.

Explanation

Procedure used:

The sum of interior angles of the triangle is 180°.

If the measure of one angle of a triangle is greater than the measure of a second angle, than the side opposite to the larger angle is longer than the side opposite to the smaller angle.

Given:

The quadrilateral ABCD is shown in the figure below,

Figure (1)

Calculation:

From the given figure (1),

Consider the triangle ΔACD.

Write the equation to calculate the sum of angles of the triangle.

DAC+ACD+D=180° (1)

Substitute 80° for ACD and 55° for DAC in equation (1) to calculate the sum of angles of the triangle.

55°+80°+D=180°D=180°135°=45°

Since, the side opposite to the larger angle is longer and the side opposite to the smaller angle is smaller. Then,

The side DA¯ is longer and the side AC¯ is smaller

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