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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 10.4, Problem 12E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 1 to 17, complete an analytic proof for each theorem.

The median of a trapezoid is parallel to the bases of the trapezoid and has a length equal to one-half the sum of the lengths of the two bases.

To determine

To answer:

The analytic proof for the given theorem “The median of a trapezoid is parallel to the bases of the trapezoid and has a length equal to one-half the sum of the lengths of the two bases”

Explanation

Given theorem is,

The median of a trapezoid is parallel to the bases of the trapezoid and has a length equal to one-half the sum of the lengths of the two bases.

The above graph shows the trapezoid ABCD.

AB is the lower base and DC is the upper base.

P is the midpoint of AD and Q is the midpoint of BC.

Joining the points P and Q as shown in the above figure.

Coordinates of the trapezoid is A(0, 0), B(a+b+c, 0), C(a+b,d) and D(a,d).

Length of the upper base DC is a below,

DC = (a-a+b)2+(d-d)2

DC = (a-a-b)2

DC = b2=b

Length of the lower length AB is as below,

AB = a+b+c-0)2+(0-0)2

AB = (a+b+c)2=a+b+c

Midpoint of AD is as below,

AD=P=a+02,d+02

AD=P=a2,d2

Similarly, the midpoint of BC is as below,

BC=Q=a+b+c+(a+b)2,d+02

BC=Q=2

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