   Chapter 4.3, Problem 23E 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 to 24, let P = { parallelograms } ,   R = { rectangles } ,   a n d   H = { rhombi } . Classify as true or false: H ⊆ P  and  R ⊆ P

To determine

To classify:

HP and RP are true or false.

Explanation

The properties of parallelograms:

1) Opposite sides are parallel by definition.

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 by definition.

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 by definition.

3) The diagonals bisect the angles.

4) The diagonals are perpendicular bisectors of each other...

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