Question

Give the most descriptive name for quadrilateral MNOP.

$\overline{\mathit{M}\mathit{N}}\cong \overline{\mathit{P}\mathit{O}};\overline{\mathit{M}\mathit{N}}\parallel \overline{\mathit{P}\mathit{O}}$

Short answer

The most descriptive name for quadrilateral MNOP where $\overline{MN}\cong \overline{PO}$and $\overline{MN}\parallel \overline{PO}$is a parallelogram.

Step-by-step solution

Step 1. Description of step.

If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.

Step 2. Description of step.

It is being given that $\overline{MN}\cong \overline{PO}$and $\overline{MN}\parallel \overline{PO}$.

In the quadrilateral MNOP, it can be noticed that the sides $\overline{MN}$and $\overline{PO}$are the opposite sides.

As, $\overline{MN}\cong \overline{PO}$and $\overline{MN}\parallel \overline{PO}$, therefore the pair of opposite sides $\overline{MN}$and $\overline{PO}$are both congruent and parallel, therefore the quadrilateral MNOP is a parallelogram.

Step 3. Write the most descriptive name for quadrilateral MNOP.

The most descriptive name for quadrilateral MNOP where $\overline{MN}\cong \overline{PO}$and $\overline{MN}\parallel \overline{PO}$is a parallelogram.