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 90o 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.

Practice From a quadrilateral to a rectangle

Exercise #1

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

AAABBBCCCDDD100°

Video Solution

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.

Answer

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?

Video Solution

Answer

Yes.

Exercise #3

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

Video Solution

Answer

Yes.

Exercise #4

It is possible to have a rectangle with different angles?

Video Solution

Answer

No

Exercise #5

There may be a rectangle with an acute angle.

Video Solution

Answer

Not true

Exercise #1

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

Video Solution

Answer

Yes.

Exercise #2

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

Video Solution

Answer

Yes.

Exercise #3

A rectangle can have diagonals that are not equal.

Video Solution

Answer

False

Exercise #4

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

Video Solution

Answer

Yes.

Exercise #5

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

Video Solution

Answer

Yes.

Exercise #1

ABCD is a square with sides measuring 4 cm.


Is ABCD a rectangle?

444AAABBBDDDCCC

Video Solution

Answer

Yes

Exercise #2

ABCD is a Given the quadrilateral.

AD||BC

AB||CD

Is the quadrilateral a rectangle?

AAABBBCCCDDD90°

Video Solution

Answer

Yes.

Exercise #3

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

AAABBBCCCDDD30°60°

Video Solution

Answer

Yes

Exercise #4

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

AAABBBCCCDDD80°20°

Video Solution

Answer

No

Exercise #5

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

AAABBBCCCDDDEEE90°

Video Solution

Answer

Yes

Topics learned in later sections

  1. From a Parallelogram to a Rectangle