Chapter 4.3, Problem 6E

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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

Rhombus *ABCD* has congruent sides

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