From a Parallelogram to a Rectangle - Examples, Exercises and Solutions

From the Parallelogram to the Rectangle

Do you want to know how to prove that the parallelogram in front of you is actually a rectangle?
First, you should know that the formal definition of a rectangle is a parallelogram whose angle is $90^o$ degrees.
Additionally, if the diagonals in parallelograms are equal, it is a rectangle.

That is, if you are given a parallelogram, you can prove it is a rectangle using one of the following theorems:

• If a parallelogram has an angle of $90^o$ degrees, it is a rectangle.
• If the diagonals are equal in a parallelogram, it is a rectangle

We briefly remind you of the conditions for a parallelogram check:

1. If in a quadrilateral where each pair of opposite sides are also parallel to each other, the quadrilateral is a parallelogram.
2. If in a quadrilateral where each pair of opposite sides are also equal to each other, the quadrilateral is a parallelogram.
3. If a quadrilateral has a pair of opposite sides that are equal and parallel, the quadrilateral is a parallelogram.
4. If in a quadrilateral the diagonals cross each other, the quadrilateral is a parallelogram.
5. If a quadrilateral has two pairs of equal opposite angles, the quadrilateral is a parallelogram.

Examples with solutions for From a Parallelogram to a Rectangle

Exercise #1

Is the parallelogram below a rectangle?

Step-by-Step Solution

The parallelogram in the drawing cannot be a rectangle because in a rectangle all angles are right angles, meaning they are equal to 90 degrees.

Angle A is greater than 90 degrees.

No

Exercise #2

Is the parallelogram below a rectangle?

Step-by-Step Solution

Let's calculate angle B:

$64+26=90$

The parallelogram in the drawing is indeed a rectangle since a parallelogram with at least one right angle is a rectangle.

Yes

Exercise #3

Is the parallelogram below a rectangle?

Step-by-Step Solution

Let's calculate angle A:

$92+33=125$

The parallelogram in the diagram is not a rectangle since angle A is greater than 90 degrees, and in a rectangle all angles are right angles.

No

Exercise #4

The quadrilateral ABCD is a parallelogram.

$∢B=90°$

Is it a rectangle?

Yes.

Exercise #5

Is this parallelogram a rectangle

No

Exercise #6

Is this parallelogram a rectangle?

Yes

Exercise #7

The quadrilateral ABCD is a parallelogram.

Is the parallelogram a rectangle?

Video Solution

Yes, a parallelogram with equal diagonals is a rectangle.

Exercise #8

Perhaps all parallelogram is also a rectangle?

Video Solution

No, a rectangle necessarily has angles of 90°.

Exercise #9

Given the following parallelogram:

Is it a rectangle?

No

Exercise #10

Side DA is equal to side DE.

Is the parallelogram a rectangle?