   Chapter 4.3, Problem 24E 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

For Exercises 21 t 24, let P = { parallelograms } ,   R = { rectangles } ,   a n d   H = { rhombi } . Classify as true or false: R ∪ H = P  and  R ∩ H = ∅

To determine

To classify:

RH=P and RH= are true or false.

Explanation

The properties of parallelograms:

1) Opposite sides are parallel.

2) Opposite sides are congruent.

3) Opposite angles are congruent.

4) Consecutive angles are supplementary.

5) The diagonals bisect each other.

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.

3) The diagonals are congruent.

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.

3) The diagonals bisect the angles.

4) The diagonals are perpendicular bisectors of each other.

Calculation:

Given:

P: set of parallelograms

R: set of rectangles

H: set of rhombi

Now we have to classify RH=P and RH= are true or false.

To check:

(1) RH=P

From the properties we note that a rhombus is a parallelogram with adjacent congruent sides

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