# From a Quadrilateral to a Rectangle - Examples, Exercises and Solutions

How do we recognize that the quadrilateral in front of us is actually a rectangle?
In two quite simple ways!

## First form: angle check

A rectangle is a quadrilateral whose angles are equal to $90^o$ degrees, if we can prove that this is also the case for our quadrilateral, we can prove that it is a rectangle.

## Second form: parallelogram proof and then rectangle proof

This form is a bit more complicated, as it involves two steps.
So, why is it useful?
There are five ways to prove that a quadrilateral is a parallelogram, so many times (depending on the data) it will be easier to prove that the quadrilateral is a parallelogram.
Once we have been able to prove this, we can move on to the next step and prove why this parallelogram is a rectangle.
Remember, a rectangle is a special case of a parallelogram.

1. Rectangle

## Examples with solutions for From a Quadrilateral to a Rectangle

### Exercise #1

Indicate if the quadrilateral is a rectangle.

### Step-by-Step Solution

In a rectangle, it is known that all angles measure 90 degrees.

Since we know that angle B is equal to 100 degrees, the quadrilateral cannot be a rectangle.

No

### Exercise #2

It is possible to draw a quadrilateral that is not a rectangle, with the sum of its two adjacent angles equaling 180?

Yes.

### Exercise #3

It is possible to draw a quadrilateral that is not a rectangle and that has two equal opposite sides?

Yes.

### Exercise #4

It is possible to have a rectangle with different angles?

No

### Exercise #5

There may be a rectangle with an acute angle.

Not true

### Exercise #6

It is possible to draw a quadrilateral that is not a rectangle and that has two opposite parallel sides?

Yes.

### Exercise #7

It is possible to draw a quadrilateral that has opposite angles and is not a rectangle?

Yes.

### Exercise #8

A rectangle can have diagonals that are not equal.

False

### Exercise #9

It is possible to draw a quadrilateral that is not a rectangle and that has diagonals which are not perpendicular to each other?

Yes.

### Exercise #10

It is possible to draw a quadrilateral that is not a rectangle and has diagonals that cross?

Yes.

### Exercise #11

ABCD is a square with sides measuring 4 cm.

Is ABCD a rectangle?

Yes

### Exercise #12

ABCD is a Given the quadrilateral.

AB||CD

Yes.

### Exercise #13

Given the quadrilateral ABCD so that

Indicate if the quadrilateral is a rectangle.

Yes

### Exercise #14

Given the quadrilateral ABCD so that

Indicate if the quadrilateral is a rectangle.

No

### Exercise #15

Given the quadrilateral ABCD so that