Question

Give the most descriptive name for quadrilateral MNOP.

$\overline{MN}\parallel \overline{PO}\mathit{;}\mathit{}\overline{NO}\parallel \overline{MP}\mathit{;}\mathit{}\overline{MO}\perp \overline{NP}$

Short answer

The most descriptive name for quadrilateral MNOP where $\overline{MN}\parallel \overline{PO}\mathit{,}\mathit{}\overline{NO}\parallel \overline{MP}$and $\overline{MO}\perp \overline{NP}$is a rhombus.

Step-by-step solution

Step 1. Description of step.

In a rhombus the pair of opposite sides are parallel and the diagonals bisect each other at a right angle.

Step 2. Description of step.

It is being given that $\overline{MN}\parallel \overline{PO}$, $\overline{NO}\parallel \overline{MP}$and $\overline{MO}\perp \overline{NP}$.

In the quadrilateral MNOP, it can be noticed that the sides $\overline{MN}$, $\overline{PO}$are the opposite sides and $\overline{NO}$, $\overline{MP}$are the opposite sides and $\overline{MO}$, $\overline{NP}$are the diagonals.

As, $\overline{MN}\parallel \overline{PO}$, $\overline{NO}\parallel \overline{MP}$and $\overline{MO}\perp \overline{NP}$, therefore the pair of opposite sides are parallel and the diagonals intersect each other at right angles, therefore the quadrilateral MNOP is a rhombus.

Step 3. Write the most descriptive name for quadrilateral .

The most descriptive name for quadrilateral MNOP where $\overline{MN}\parallel \overline{PO}$, $\overline{NO}\parallel \overline{MP}$and $\overline{MO}\perp \overline{NP}$is a rhombus.