   Chapter 10.3, Problem 8E 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 5 to 10, the real numbers a, b, c, and d are positive.Consider the quadrilateral with vertices at A 0 ,   0 , B a ,   0 , C b ,   c , and D d ,   c . Explain why A B C D is a trapezoid. To determine

To explain:

ABCD is a trapezoid.

Explanation

The given diagram is shown below.

To prove ABCD is a trapezoid, we have to prove the following statement.

Only one pair of opposite sides are parallel.

AB is parallel to DC.

That is slope of AB is equal to slope of DC.

AD is not parallel to BC.

That is slope of AD is not equal to slope of BC.

Find the slope of AB.

x1,y1=A0, 0

x2,y2=Ba, 0

Formula for slope joining the line segment.

Slope is denoted by m.

m=y2-y1x2-x1

Here x1x2

Substituting the x and y co-ordinates.

mAB=0-0a-0

mAB=0

Then, find the slope of DC.

x1,y1=Dd, c

x2,y2=Cb, c

Substituting the x and y co-ordinates.

mDC=c-cb-d

mDC=0b-d

mDC=0

mAB=mDC

Hence, AD and BC are parallel

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