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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 25 to 36, 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 ¯

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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