Using the properties of a parallelogram, can you determine which are parallelograms? Answer choices are in the picture.

The following figures are parallelograms:

Figure A

Figure B

Figure E

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, choices 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.