Question

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Short answer

No, the given figure ABCD is not a parallelogram.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

From the given diagram it can be noticed that:

$AB=CD$and $OB=OD$.

Therefore, $AB\cong CD$and $OB\cong OD$.

That implies the one pair of opposite sides of the quadrilateral is congruent and one of the diagonal is bisecting.

Neither the two pairs of opposite sides are parallel, one pair of opposite sides are congruent and parallel, nor the two diagonals bisect each other.

Therefore, the given quadrilateral ABCD is not a parallelogram.

Step 3. Write the conclusion.

No, the given figure ABCD is not a parallelogram.