   Chapter 6.1, Problem 21E 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

Suppose that a circle is divided by points A , B , C , and D into four congruent arcs. What is the measure of each arc? If these points are joined in order, what type of quadrilateral results?

To determine

To Find:

The measure of each arc. If these points are joined in order, determine the type of quadrilateral results.

Explanation

Given:

Since, a circle is divided by points A, B, C, and D into four congruent arcs.

Definition:

Congruent arcs:

In a circle, congruent arcs are arcs with equal measures.

Since, the sum of the measures of the consecutive arc that form a circle is 360o.

Calculation:

Since, in a circle, congruent arcs are arcs with equal measures.

mAB=mBC

mBC=mCD

mCD=mDA

And

mAB=mDA

Since, the sum of the measures of the consecutive arc that form a circle is 360o.

mAB+mBC+mCD+mDA=360o

By using the above result we obtain

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