How do we recognize that the quadrilateral in front of us is actually a rectangle?

In two quite simple ways!

How do we recognize that the quadrilateral in front of us is actually a rectangle?

In two quite simple ways!

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.

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.

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

Many times we are asked to prove that the quadrilateral we see is a rectangle, or we will need it to continue with our solution.** To prove that a quadrilateral is a rectangle, we can proceed with the proof in one of two ways:**

If in the quadrilateral in front of you there are $3$ angles equal to $90^o$ degrees each, you can determine that this quadrilateral is a rectangle.

It is not necessary to verify the fourth angle since we know that the sum of the internal angles in the quadrilateral is $360^o$ degrees and equal to $90^o$ degrees.

Test your knowledge

Question 1

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

Question 2

It is possible to have a rectangle with different angles?

Question 3

There may be a rectangle with an acute angle.

This form is a bit more complex and first you must verify that the quadrilateral in front of you is a parallelogram.** We briefly remind you of the conditions to prove a parallelogram:**

- If in a quadrilateral each pair of opposite sides are also parallel to each other, the quadrilateral is a parallelogram.
- If in a quadrilateral each pair of opposite sides are also equal to each other, the quadrilateral is a parallelogram.
- If in a quadrilateral each pair of opposite sides are equal and parallel, the quadrilateral is a parallelogram.
- If in a quadrilateral, the diagonals intersect the quadrilateral is a parallelogram.
- If in a quadrilateral there are two pairs of equal opposite angles, the quadrilateral is a parallelogram.

Have you proven that the quadrilateral in front of you is a parallelogram using one of the previous conditions?

Excellent!

You can continue with the next step** Now, you must prove that the parallelogram in front of you is a rectangle using one of these two conditions:**

- If the parallelogram has a 90-degree angle, it is a rectangle.
- If the diagonals are equal in the parallelogram, it is a rectangle.

Wonderful! Now you know all the ways to prove that this is not an ordinary quadrilateral, but a rectangle.

**If you are interested in this article, you might be interested in the following articles:**

Rectangles with Equivalent Area and Perimeter

Congruence of Right Triangles (in the context of the Pythagorean Theorem)

From a Quadrilateral to a Rectangle

From a Parallelogram to a Rectangle

**In the blog of** **Tutorela** **you will find a variety of articles about mathematics.**

Given the quadrilateral ABCD whereby

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

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

Yes.

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

Yes.

It is possible to have a rectangle with different angles?

No

There may be a rectangle with an acute angle.

Not true

Do you know what the answer is?

Question 1

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

Question 2

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

Question 3

A rectangle can have diagonals that are not equal.

Related Subjects

- Area
- Trapezoids
- Symmetry in Trapezoids
- Diagonals of an isosceles trapezoid
- Types of Trapezoids
- Isosceles Trapezoid
- Parallelogram
- Identifying a Parallelogram
- Rotational Symmetry in Parallelograms
- From the Quadrilateral to the Parallelogram
- Kite
- Rectangle
- From a Parallelogram to a Rectangle
- Calculating the Area of a Rectangle
- The perimeter of the rectangle
- Congruent Rectangles
- Square
- Area of a square
- From Parallelogram to Square
- Rhombus, kite, or diamond?
- Diagonals of a Rhombus
- Lines of Symmetry in a Rhombus
- From Parallelogram to Rhombus
- The Area of a Rhombus
- Perimeter