Only when they are isosceles trapezoids.
No. If it did it would be a rectangle. A trapezoid only has two congruent sides.
A parallelogram has two pairs of congruent sides.
A parallelogram has two pairs of congruent sides, and the opposite sides are congruent.
A parallelogram has two pairs of congruent sides.
A rectangle has two pairs of parallel and congruent sides. An equilateral rectangle, or square, has four equal sides. Other quadrilaterals include trapezoids, which have two adjacent and equal sides, parallelograms, which have two pairs of parallel and congruent sides, and rhombi, which have four equal sides. (The a rectangle is a type of parallelogram. What differentiates it is angle configuration. A rhombus is likewise differentiated from a square by angle configuration.)
By definition, all trapezoids must have one pair of parallel sides. Therefore, an isosceles has one pair of congruent angles.
rectangle
Diamond
Yes, but in fact, all four (two pairs of two) are congruent.
No, a parallellogram is a quadrilateral with two pair of congruent sides and a trapezoid is a quadrilateral with only one pair of congruent sides.
A square
Two pairs of adjacent sides are congruent. The angles between the non-congruent sides are congruent.