   Chapter 6.4, 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

Prove: In a circle containing two unequal arcs, the longer arc corresponds to the larger central angle.

To determine

To prove:

The given statement.

Explanation

Given:

The statement,

“In a circle containing two unequal arcs, the longer arc corresponds to the larger central angle.”

Assume O with two arcs mAB, mCD and mAB>mCD.

The angle corresponding to arc mAB is 1 and the angle corresponding to arc mCD is 2.

To Prove:

To prove that the given statement is correct:

“In a circle containing two unequal arcs, the longer arc corresponds to the larger central angle.”

To prove that: m1>m2.

Property Used:

According to the following property,

The angle measure of the central angle is congruent to the measure of the intercepted arc.

Proof:

Since mAB>mCD and from the figure below,

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