No not even as an isosceles trapezoid
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An isosceles triangle has no parallel sides but it does have two equal sides
It can do. The non-parallel sides of an isosceles trapezium will be equal. Also, one of the non-parallel sides could be equal to one of the parallel sides.
Called an Isosceles trapezoid when the sides that aren't parallel are equal in length.
No but the diagonals are equal in length
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.