   Chapter 4.3, Problem 18E 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 15 to 18, consider rhombus ABCD with diagonals A C ¯  and  D B ¯ . When the answer is not a whole number, leave a square root answer. Exercises 15 – 18If AC = 14 and DB = 10, find BC.

To determine

To find:

BC of the given rhombus.

Explanation

The basic properties of rhombus:

1) All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary).

2) All sides are congruent by definition.

3) The diagonals bisect the angles.

4) The diagonals are perpendicular bisectors of each other.

Calculation:

Given: AC = 14 and DB = 10

Consider the rhombus.

To find BC:

From the property, in rhombus, two diagonals are perpendicular bisectors of each other.

In rhombus ABCD,

AE=EC=AC2=142=7

DE=EB=DB2

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