Chapter 6.4, Problem 36PPS

To determine

To prove:

The following statement with the paragraph proof:

‘If a quadrilateral has four right angles, then it is a rectangle.’

Explanation of Solution

Given information:

A quadrilateral has four right angles

Proof:

A paragraph proof to prove quadrilateral is a rectangle is written as below:

Here, it is given that a quadrilateral has four right angles. Let’s consider a quadrilateral $▱\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ . It has four right angles as $\angle \mathrm{A},\angle \mathrm{B},\angle \mathrm{C},\angle \mathrm{D}$ . Here, both pairs of opposite angels are congruent therefore $▱\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is defined as parallelogram as well. Therefore, one can say that parallelogram $▱\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ has four right angles. As per definition of the rectangle when there is four right angles in the figure then it is known as a rectangle. Hence it is proved that if a quadrilateral has four right angles, then it is defined as rectangle.