   Chapter A.3, Problem 9E 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 line segments, A B > C D ( the length of segment AB is greater than that of segment CD), C D > E F , E F > G H and G H > I J . What conclusion does the Transitive Property of Inequality allow regarding IJ and AB?

To determine

To find:

To write the conclusion about the Transitive Property of Inequality allow regarding IJ and AB by using the given condiiton,

Explanation

Consider the following condition,

“Of several line segments, AB>CD (the length of segment AB is greater than that of segment CD), CD>EF, EF>GH and GH>IJ.”

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 AB>CD or CD<AB then by using the definition to get CD+p1=AB...(1)

Then, CD>EF or EF<CD then by using the definition to get EF+p2=CD ...(2)

Then EF>GH or GH<EF then by using the definition to get GH+p3=EF...(3)

Then GH>IJ or IJ<GH then by using the definition to get IJ+p4=GH ...(3)

Substitute (3) in (4) to get the following,

GH+p3=EFIJ+(p4+p3)=EF

Substitute the above equaiton in equation (2) to get the following,

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