Search 73,881 tutors
0 0

# does a quadrilateral have to have four congruent sides

does a quadrilateral have to have four congruent sides

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.

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

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.