Question

If BE ≅ LU in quadrilateral BLUE shown, which additional information would be sufficient to prove quadrilateral BLUE is a parallelogram?
A) BL || EU

B) LU || BE

C) BE ≅ BL

D) LU ≅ EU

Which statement is NOT always true about a parallelogram?

A) The diagonals are congruent.

B) The opposite sides are congruent.

C) The opposite angles are congruent.

D) The opposite sides are parallel.

Answer 1

Answer: Option A and option B would be sufficient to prove that BLUE is a parallelogram. The diagonals are congruent IS NOT ALWAYS TRUE about a parallelogram.

Step-by-step explanation: Please refer to the diagram attached for details. One of the properties of a parallelogram is that each pair of opposite sides are equal to each other. So lines BE and LU are parallel as shown by the arrows on both lines in the attached picture. Same applies to lines BL and EU. Line BE doesn’t have to be congruent to BL, but BE must be congruent to LU. Same applies to BL and EU. Also in a parallelogram, opposite sides are congruent, opposite angles are congruent (angle B = angle U and angle E = angle L) and opposite sides are parallel. The diagonals are NOT ALWAYS congruent. This is only possible if all four sides are of the same measurement. However if for instance, side BE does not equal BL, then the diagonals cannot be equal.