   Chapter A.3, Problem 10E 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

Of several angles, the degree measures are related in this way: m ∠ J K L > m ∠ G H I (the measure of the angle JKL is greater than that of angle GHI), m ∠ G H I > m ∠ D E F and m ∠ D E F > m ∠ A B C . What conclusion does the Transitive Property of Inequality allow regarding m ∠ A B C and m ∠ J K L ?

To determine

To write:

The conclusion about the Transitive Property of Inequality allow regarding mABC and mJKL by using the given condiiton.

Explanation

Consider the following condition,

“Of several angles, the degree measures are related in this way: mJKL>mGHI (the measure of the angle JKL is greater than that of angle GHI), mGHI>mDEF and mDEF>mABC.”

Definition:

If a is less than b a<b if and only if there is a positive number p for which

a+p=b;

a is greater than b a>b if and only if b<a.

Transitive Property of Inequality:

For number a, b, and c, if a<b and b<c, then a<c.

First mJKL>mGHI then by using the definition to get mJKL=mGHI+p1...(1)

Then, mGHI>mDEF then by using the definition to get mGHI=mDEF+p2...(2)

Then mDEF>mABC then by using the definition to get mDEF=mABC+p3..

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