True or False?: If a quadrilateral has EXACTLY 3 congruent sides and the 4th side is parallel to one of the other sides, then the figure must be an isosceles trapezoid.

Answer 1

False

If three sides are congruent, and the fourth side is parallel to one of the three sides, then it cannot be an isosceles rather 3 sides equal trapezoid.

Answer 2

The trapezoid the previous tutor described is still an isosceles trapezoid (even with 3 sides equal).

There are 2 cases to consider.

If the two parallel sides are also equal, then what shape would you get? You would get a parallelogram with 4 equal sides (rhombus) which violates the condition of the problem which says "EXACTLY 3 sides equal".

If the two parallel sides are not equal, then the other two sides must be equal and also equal to one of the two parallel sides. Then you would end up with a trapezoid with 3 equal sides as the previous tutor described. However, this is still an isosceles trapezoid. The word "isosceles" only refers to the fact that the nonparallel sides are equal. It is okay if they are also equal to one of the parallel sides.

This means the statement is true.