Chapter 4.3, Problem 20E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

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

# Given: Rhombus RSTV (not shown) with diagonals R T ¯  and  S V ¯ so that RT = 8 and SV = 6 Find: RS, the length of a side

To determine

To find:

RS, the length of a side.

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: Rhombus RSTV with diagonals RTÂ¯Â andÂ SVÂ¯.

RT = 8 and SV = 6

Consider the rhombus.

To find RS:

From the property, in rhombus, diagonals are perpendicular bisectors.

In rhombus RSTV

RA=AT=RT2=82=4

V

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