The following figures are parallelograms:
Figure A
Figure B
Figure E
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Explanation:
If the diagonals of the quadrilateral are the same length (aka congruent), then we can prove that we have the opposite sides parallel. That would conclude in the figure being a parallelogram. Therefore, choice A is a parallelogram because of this fact. Choice C is not a parallelogram because of this.
Also, recall that parallelograms have their opposite sides being the same length. Think of a rectangle, but we can slant the sides as figure B shows. Figure B is a parallelogram due to the opposite sides being the same length. More specifically, it's a rhombus (because all four sides are the same). Any rhombus is a parallelogram, but not the other way around.
One last useful property we'll use is the fact that adjacent angles of a parallelogram are supplementary. This means the angles add to 180. In figure D, the adjacent angles add to 74+105 = 179, which isn't 180. So we rule out choice D. Choice E works though because 55+125 = 180.
