   Chapter 4.3, Problem 6E 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

If the diagonals of a quadrilateral are perpendicular bisectors of each other (but not congruent), what can you conclude regarding the quadrilateral?

To determine

To conclude:

If the diagonals of a quadrilateral are perpendicular bisectors of each other (but not congruent).

Explanation

The 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:

Consider the quadrilateral with the diagonals are perpendicular and bisecting each other but not congruent.

Let us consider the above as rhombus ABCD, with diagonals AC¯ and DB¯

Rhombus ABCD has congruent sides

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