Chapter 6.4, Problem 35PPS

To determine

To prove:

The following statement with the paragraph proof:

‘If a parallelogram has one right angle, then it is a rectangle.’

Explanation of Solution

Given information:

A parallelogram has one right angle

Proof:

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

Here, it is given that a parallelogram has one right angle. Let’s consider a parallelogram $▱\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ . It has one right angle $\angle \mathrm{B}$ . Know that if one of the angles of a parallelogram is a right angle then the remaining angles are also right angles. Therefore, one can say that $▱\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ has four right angles as $\angle \mathrm{A},\angle \mathrm{B},\angle \mathrm{C},\angle \mathrm{D}$ . 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 parallelogram has one right angle, then it is a rectangle.