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# does a quadrilateral have to have four congruent sides

does a quadrilateral have to have four congruent sides

### 3 Answers by Expert Tutors

Cristina G. | Need help in Math, Science, Social Studies, and Spanish??Need help in Math, Science, Social Studi...
4.9 4.9 (11 lesson ratings) (11)
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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.

Kevin S. |
5.0 5.0 (4 lesson ratings) (4)
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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.

Thanks Kevin!

Bill F. | Experienced Teacher & Tutor in Round Rock, TXExperienced Teacher & Tutor in Round Roc...
5.0 5.0 (1 lesson ratings) (1)
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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