   Chapter 4.CR, Problem 31CR 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

Review Exercises Construct rhombus ABCD, given these lengths for the diagonals. To determine

To Construct:

Draw the rhombus using the measures of its diagonals.

Explanation

Definition:

A rhombus is a parallelogram with two congruent adjacent sides.

Properties:

1. All sides of a rhombus are congruent.

2. The diagonals of a rhombus are perpendicular.

3. The diagonals of a rhombus are perpendicular bisector of each other.

Description:

From the provided lines, it can be measured that AC=3 cm and BD=4 cm.

Let’s construct the rhombus using its diagonal lengths with the help of definition and properties of rhombus.

As the diagonals of the rhombus are perpendicular bisector of each other at O, both lines meets at 90° each other and bisecting at its midpoint.

Let’s consider the right AOB.

Applying Pythagorean theorem,

AB2=AO2+OB2

AB2=(1

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