   Chapter 6.1, Problem 36E 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.An angle inscribed in a semicircle is a right angle.

To determine

To prove:

The statement “An angle inscribed in a semicircle is a right angle”.

Explanation

Given:

The provided statement is “An angle inscribed in a semicircle is a right angle”.

Theorem used:

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

Proof:

Consider a circle with center O.

Let RT¯ be the diameter.

Let S and V be the points in the circle as shown below.

From the figure, we see that RST is the semicircle and S is the inscribed angle.

Also we see that S intercepts the semicircle RVT

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