   Chapter 4.3, Problem 19E 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

Given: ABCD (not shown) with AB = 8 and BC = 6; M and N are the midpoints of sides A B ¯  and  B C ¯ , respectively. Find: MN

To determine

To find:

MN of the given rectangle.

Explanation

The basic properties of rectangle:

1) All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).

2) All angles are right angles by definition.

3) The diagonals are congruent.

Calculation:

Given: In Rectangle ABCD, AB = 8 and BC = 6.

M and N are the midpoints of sides AB¯ and BC¯, respectively.

Consider the rectangle.

To find MN:

From the property, in rectangle the diagonals bisect each other.

In rectangle ABCD

AM=MB=AB2=82=4

NC

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