Question

For the following figure, can you deduce from the information $\overline{AD}\left|\right|\overline{BC}$ and$\overline{AD}\cong \overline{BC}$ that quadrilateral ABCD is a parallelogram. If so, what theorem can you use?

Short answer

The quadrilateral ABCD is a parallelogram.

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the concept of parallelogram.

A quadrilateral is said to be a parallelogram when both the opposite sides are parallel.

Step 3- Step description.

Consider $\overline{AD}\left|\right|\overline{BC};\overline{AD}\cong \overline{BC}$.

Observe that these are pair of opposite sides which are given to be parallel.

Consider the fact that a parallelogram is quadrilateral with both pairs of opposite sides parallel and congruent.

From the figure of ABCD , both pairs of opposite sides to be parallel.

Thus, ABCD is a parallelogram.