A trapezoid with two congruent, opposite sides is an isosceles trapezoid.
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The answer depends on which two sides are congruent: the two non-parallel sides or a pair of adjacent sides.
A trapezoid will always have two parallel sides. However, it will not necessarily have two congruent sides. The only way it will have two congruent sides is if the angles at the base match.
A trapezoid.
Isosceles trapezoid
trapezoid * * * * * It cannot be a trapezoid because that does not have four congruent sides. In fact it need not have even two congruent sides. The correct answer is a rhombus.
A right trapezoid can have no congruent sides and two right angles.