Q: Do all trapezoids have one pair of congruent sides?

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No. Most trapezoids don't even have one pair of congruent sides. Only isosceles trapeoids have one pair; none have more than one pair.

By definition, all trapezoids must have one pair of parallel sides. Therefore, an isosceles has one pair of congruent angles.

they have to because if they didn't it would be some sort of pentagon. so... yes

Yes.

"It is a quadrilateral with exactly one pair of parallel sides." is the true one. Some people define it as having at least one pair of parallel sides, so if your teacher is one of those people then all of the answers are wrong, but since all of the other answers are definitely wrong then this is the only one that could be right.

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By definition, a trapezoid only must have exactly one pair of parallel sides. An isosceles trapezoid does have one pair of congruent sides, but not all trapezoids will have exactly one pair of congruent sides.

No. Most trapezoids don't even have one pair of congruent sides. Only isosceles trapeoids have one pair; none have more than one pair.

Only if it's an isosceles trapezoid otherwise all trapezoids have exactly one pair of parallel sides that are of different lengths

Because the top and the bottem are not the same size

By definition, all trapezoids must have one pair of parallel sides. Therefore, an isosceles has one pair of congruent angles.

they have to because if they didn't it would be some sort of pentagon. so... yes

No. Most Trapezoids are not isosceles. The non parallel sides must be congruent to be isosceles.

There are: Squares, which have all four sides parallel and congruent, all four angles are right and congruent, the diagonals bisect each other and are congruent. Trapezoids, which have two of their sides parallel Rhombus, which have all sides congruent, diagonals bisect, and opposite angles are congruent Parallelograms, which have opposite sides congruent and parallel, diagonals bisect Rectangle, which is a square but one pair of opposite sides aren't congruent.

Yes.

"It is a quadrilateral with exactly one pair of parallel sides." is the true one. Some people define it as having at least one pair of parallel sides, so if your teacher is one of those people then all of the answers are wrong, but since all of the other answers are definitely wrong then this is the only one that could be right.

No, trapezoids are not rectangles. While both shapes have four sides, rectangles have opposite sides that are equal in length and all interior angles are right angles, whereas trapezoids have only one pair of opposite sides that are parallel.

Yup :p