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does a quadrilateral have to have four congruent sides

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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.

 

 

Comments

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.

 

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

Bill, a parallelogram does NOT necessarily have to have 4 congruent sides. Only RHOMBUSES and squares, subsets of parallelograms, have 4 congruent sides