   Chapter 6.1, Problem 35E 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.A radius perpendicular to a chord bisects the arc of that chord.

To determine

To prove:

The statement “A radius perpendicular to the chord bisects the arc of that chord”.

Explanation

Given:

The provided statement is “A radius perpendicular to the chord bisects the arc of that chord”.

Theorem used:

Hypotenuse Leg theorem:

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and the leg of a second right triangle, then the triangles are congruent.

Proof:

Consider a circle with center O. Let AB¯ be the chord and OD¯ be the radius.

We have to prove the radius perpendicular to the chord bisects the arc of that chord. That is to prove OD¯ bisects AB¯.

Draw radii OA¯ and OB¯.

Consider the triangles OCA and OCB.

Since the radii of the circle are equal, we can say OA¯OB¯

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 