   Chapter 6.4, Problem 6E 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 1 to 8, use the figure provided.If m ∠ C Q D < m ∠ A Q B , write an inequality that compares Q M to Q N . To determine

To write:

An inequality that compares QM to QN.

Explanation

Given:

mCQD<mAQB and the figure given below

Theorem:

In a circle (or in congruent circles) containing two unequal central angles, the larger angle corresponds to the larger intercepted arc.

In a circle (or in congruent circles) containing two unequal chords, the shorter chord is at the greater distance from the center of the circle.

In a circle (or in congruent circles) containing two unequal minor arcs, the greater minor arc corresponds to the longer of the chords related to these arcs.

Calculation:

Using the theorem.

Since the angles are unequal i.e. mCQD<mAQB and from the given figure

The arc corresponding to angle mCQD is mCD and the arc corresponding to angle mAQB is mAB, we conclude that mCD<mAB.

Now applying the theorem:

And since the arcs are unequal i.e. mCD<mAB and from the given figure

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