Question

Must quad. EFGH be a parallelogram? Can it be a parallelogram? Explain.

Short answer

EFGH is a not parallelogram.

Step-by-step solution

Step 1. Properties of a parallelogram

It is known that a parallelogram is a quadrilateral whose both pairs of opposite sides are parallel.

Step 2. Check the pair of equal angles

It can be observed from the above figure that the opposite angles $\angle HEF$and $\angle HGF$are not congruent.

Step 3. Check whether EFGH is a parallelogram

As discussed above that, the pair of the opposite angles are not equal.

So by theorem 5-2 which states that the relationship between two angles that are related to a parallelogram and positioned on the opposite side of each other is congruent, it can be said that EFGH is not a parallelogram.