Question

Is the following shape a parallelogram? If so, which condition proves it ?
A. Both pairs of opposite sides are parallel ( definition )
B. One pair of opposite sides are parallel and congruent
C. Both pairs of opposite sides are congruent
D. Both pairs of opposite angles are congruent
E. One angle is supplementary of both sides of its consecutive angles
F. The diagonals bisects each other

Answer 1

Answer:

B and F

Step-by-step explanation:

Option A is false, there is no information whether opposite sides are parallel.

Option B is true because of following parallelogram theorem.

Parallelogram theorem: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.

Option C is false, there is no information about any angles.

Option D is false, there is no information about any angles.

Option E is false, there is no information about any angles.

Option F is true because of following parallelogram theorem.

Parallelogram theorem:  If a quadrilateral has diagonals which bisect each other, then it is a parallelogram.