No.
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It has one pair of opposite angles that are equal but not two.
the sides that are parallel of each other are equal. * * * * * True, but that was not the question! In general, the diagonals are not of equal length.
they are called parallelogram in which diagonals are equal
An isosceles trapezoid will have diagonals of equal length but will never contain right angles by definition. A square and rectangle will have diagonals of equal length but will contain 4 right angles. A rhombus and any other parallelogram that does not contain right angles will not have diagonals of equal length.
Yes.