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

In two quite simple ways!

Question Types:

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.

Question 1

Given the quadrilateral ABCD whereby

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

Question 2

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

Question 3

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

Question 4

It is possible to have a rectangle with different angles?

Question 5

There may be a rectangle with an acute angle.

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

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

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

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.

Question 4

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

Question 5

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

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

Yes.

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

Yes.

A rectangle can have diagonals that are not equal.

False

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

Yes.

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

Yes.

Question 1

ABCD is a square with sides measuring 4 cm.

Is ABCD a rectangle?

Question 2

ABCD is a Given the quadrilateral.

AD||BC

AB||CD

Is the quadrilateral a rectangle?

Question 3

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

Question 4

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

Question 5

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

ABCD is a square with sides measuring 4 cm.

Is ABCD a rectangle?

Yes

ABCD is a Given the quadrilateral.

AD||BC

AB||CD

Is the quadrilateral a rectangle?

Yes.

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

Yes

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

No

Given the quadrilateral ABCD so that

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

Yes