No but the diagonals are equal in length
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Called an Isosceles trapezoid when the sides that aren't parallel are equal in length.
No not even as an isosceles trapezoid
No. All trapezoids have only one pair of parallel sides which are different in length. In an isosceles trapezoid the lengths of the two non-parallel sides are equal.
Yes the non parallel sides of an isosceles trapezoid are congruent
No because otherwise it would be a rectangle