does a quadrilateral have to have four congruent sides

## does a quadrilateral have to have four congruent sides

# 3 Answers

No. A quadrilateral is simply a 4 sided polygon. There are 2 special subsets of polygons. The first is a trapezoid, which has 1 pair of opposite sides being parallel. If the other two pairs of base angles and opposite sides are congruent, then the trapezoid is isosceles. The four sides in a trapezoid are NEVER congruent.

The other special subset of quadrilaterals is parallelograms. A parallelogram has opposite sides being both congruent and parallel. Opposite angles are also congruent and consecutive angles are supplementary (= 180). Subsets of parallelograms are rectangles, where all the angles are right angles (=90) and rhombuses, which DO have all 4 sides being congruent. A special quadrilateral that is BOTH a rhombus and a rectangle is the square.

In short, only squares and rhombuses have 4 congruent sides. The rest do not.

Addition to Bill's answer: If all 4 sides were equal/congruent, it would be a square or a rhombus.

A rhombus is a parallelogram that has all 4 sides congruent, and opposite angles congruent (not necessarily 90 degrees). A parallelogram only has to have opposite sides congruent.

A square is a rhombus with 90 degree angles.

# Comments

Thanks Kevin!

Hi Natalei... short answer: No! By definition, a quadrilateral is any 4-sided figure. If all 4 sides were equal, it would be either a square, or a parallelogram

## Comments

I couldn't top your explanation :-D. So I didn't post an answer. I voted for yours instead.

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