   Chapter 4.CR, Problem 19CR 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

Review Exercises In isosceles trapezoid D E F G , D E - ∥ G F - and m ∠ D = 108 ° . Find the measures of the other angles in the trapezoid.

To determine

To Find:

The measure of the angles in the trapezoid DEFG with help of the information provided.

Explanation

Properties Used:

1. In an isosceles trapezoid, the two base angles are congruent.

2. Diagonals of an isosceles trapezoid are congruent.

3. Each pairs of leg angles of an isosceles trapezoid are supplementary.

Definition:

A trapezoid is a quadrilateral with exactly two parallel sides.

Calculation:

It is given that DEFG is an isosceles trapezoid with DE-GF- and mD=108°.

Therefore, the lines DE- and GF- must be the parallel bases of the isosceles trapezoid DEFG.

By the property of an isosceles trapezoid, that is ‘base angles are congruent’ mD=mE=108° and mG=mF

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