does a quadrilateral have to have four congruent sides Solut

does a quadrilateral have to have four congruent sides ?

Solution

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.