Is the following biconditional true? A quadrilateral is an isosceles trapezoid if and only if it has a pair of opposite congruent sides. yes

The statement is indeed true! An isosceles trapezoid is defined as a trapezoid with at least one pair of opposite sides that are both parallel and congruent. This uniqueness means that if you have a quadrilateral with one pair of opposite congruent sides, it can be classified as an isosceles trapezoid. However, it's worth noting that while all isosceles trapezoids possess a pair of congruent sides, the converse is not universally true—some quadrilaterals might have a pair of congruent sides without being isosceles trapezoids, like certain parallelograms. So, it's essential to consider the full shape to ensure it adheres to the definition of an isosceles trapezoid!