   Chapter 6.1, 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

In Exercises 32 to 37, write a paragraph proof.If two inscribed angles intercept the same arc, then these angles are congruent.

To determine

To prove:

The statement “If two inscribed angles intercept the same arc, then these angles are congruent”.

Explanation

Given:

The provided statement is “If two inscribed angles intercept the same arc, then these angles are congruent”.

Theorem used:

The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc.

Proof:

Consider two inscribed angles intercepted by the same arc.

The pictorial representation is shown below

Here 1 and 2 are the two inscribed angles with the same intercepted arc AB.

To prove: 12

From the figure we see that 1 is intercepted by AB.

m1=12mAB

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