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Elementary Geometry for College St...

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

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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 23 to 35, give the indirect proof for each problem or statement.

Given: M B > B C
A M = C D
Prove: B is not the
midpoint of A D ¯

Chapter 2.2, Problem 26E, In Exercises 23 to 35, give the indirect proof for each problem or statement. Given: MBBC AM=CD

To determine

To prove:

The given statement.

Explanation

Given:

The given statement is,

MB>BC and AM=CD

Figure (1)

Property:

A point B lies between the points A and C of line segment AC if and only if, AB+BC=AC.

Approach:

Assume that B is the midpoint of AD¯.

AB¯=BD¯

Point M lies between the points A and B. Point C lies between the points B and D in figure (1).

By above stated property,

AB¯=AM¯+MB¯BD¯=BC¯+CD¯AM¯+MB¯=BC¯+CD¯

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