Question

Give the most descriptive name for quadrilateral MNOP.

$\angle M\cong \angle N\cong \angle O\cong \angle P$

Short answer

The most descriptive name for quadrilateral MNOP where $\angle M\cong \angle N\cong \angle O\cong \angle P$is a square or rectangle.

Step-by-step solution

Step 1. Description of step.

In square and rectangle, all the angles have a measure of $90°$.

Step 2. Description of step.

It is being given that $\angle M\cong \angle N\cong \angle O\cong \angle P$.

As the sum of the angles of a quadrilateral is $360°$.

Therefore, the sum of the angles of the quadrilateral MNOP is $360°$.

Therefore, it can be obtained that:

$\begin{array}{c}\angle M+\angle N+\angle O+\angle P=360°\\ \angle M+\angle M+\angle M+\angle M=360°\\ 4\angle M=360°\\ \angle M=\frac{360°}{4}\\ \angle M=90°\end{array}$

As, $\angle M\cong \angle N\cong \angle O\cong \angle P$therefore, $\angle M=\angle N=\angle O=\angle P=90°$.

In the square, all the angles have a measure of $90°$.

Therefore, as in the quadrilateral MNOP, all angles are having the measure of $90°$, therefore the quadrilateral MNOP is a square.

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

The most descriptive name for quadrilateral MNOP where $\angle M\cong \angle N\cong \angle O\cong \angle P$is a square or rectangle.