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505-555 Level|   Geometry|      
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Is quadrilateral MNPQ a rectangle? 03 Jul 2014, 04:45
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Is quadrilateral MNPQ a rectangle?

(1) At least two of the four angles are right angles.
(2) At least three of the four angles are right angles.
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B
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Is quadrilateral MNPQ a rectangle? 03 Jul 2014, 05:09
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Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.
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Is quadrilateral MNPQ a rectangle? 03 Jul 2014, 05:10
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Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.
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Similar questions to practice:
is-quadrilateral-abcd-a-rectangle-156161.html
is-quadrilateral-abcd-a-rectangle-100729.html

Hope it helps.
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Is quadrilateral MNPQ a rectangle? 04 Jul 2014, 00:08
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Bunuel
Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.
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Hello Bunuel

I have a doubt here.
If all 4 angles are 90 degrees then it can be a square also.

We dont know whether all 4 sides or only 2 sides opposite sides are equal ?

So should B be the answer ?
Please correct me

Thankyou.
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Is quadrilateral MNPQ a rectangle? 04 Jul 2014, 02:48
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niyantg
Bunuel
Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.

Hello Bunuel

I have a doubt here.
If all 4 angles are 90 degrees then it can be a square also.

We dont know whether all 4 sides or only 2 sides opposite sides are equal ?

So should B be the answer ?
Please correct me

Thankyou.
Show more

All squares are rectangles so if MNPQ is a square it's a rectangle too.
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Is quadrilateral MNPQ a rectangle? 30 May 2017, 07:20
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Bunuel What if all the four angles are 90 but opposite sides are not equal?
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Is quadrilateral MNPQ a rectangle? 30 May 2017, 07:52
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Nitish7
Bunuel What if all the four angles are 90 but opposite sides are not equal?
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If all four angels are 90 degrees, then we have a rectangle, in rectangle all four angles are equal.
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Is quadrilateral MNPQ a rectangle? 30 May 2017, 22:00
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Hi Banuel,
What if I have a square and tilt it clockwise by 45 degrees.. more like a rhombus..
its not rectangle right?
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Is quadrilateral MNPQ a rectangle? 30 May 2017, 22:30
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sasidharrs
Hi Banuel,
What if I have a square and tilt it clockwise by 45 degrees.. more like a rhombus..
its not rectangle right?
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Hi

If you take a square and tilt it clockwise, it will still remain a square. When you say tilting, I assume you are just rotating that quadrilateral clockwise or anticlockwise.

A rhombus has all sides equal but all angles are not necessarily equal. So if all the angles are not equal to 90 degrees, then it will definitely not be a rectangle.
But it can surely be a rhombus.
As I wrote, a rhombus has all sides equal but all angles might not be equal, though opposite angles are always equal. A rhombus in which all angles are also equal - then becomes a square. So we say that all squares are rhombuses but all rhombuses are not squares.
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Is quadrilateral MNPQ a rectangle? 23 Mar 2023, 08:12
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Bunuel
Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.

Hello Bunuel

I have a doubt here.
If all 4 angles are 90 degrees then it can be a square also.

We dont know whether all 4 sides or only 2 sides opposite sides are equal ?

So should B be the answer ?
Please correct me

Thankyou.

All squares are rectangles so if MNPQ is a square it's a rectangle too.
Show more


Hi, can we really say all squares are rectangles ? Can you clarify some properties similar to this. I heard something similar about a square being a rhombus too ? Not sure how to understand this.

Example: I have another similar question below:

Is Quadrilateral a square?
(1) Three angles of a quadrilateral are 90 degrees each.
(2)3 sides of a quadrrilateral are equal in length.

OA: C

(1) Three angles of a quadrilateral are 90 degrees each: Then the quadrilateral can be a rectangle or a square.
(2) 3 sides of a quadrrilateral are equal in length: Then the quadrilateral can be a rhombus or a square.
(1) + (2): The quadrilateral has to be a square.

Here, point A says the same thing. However, the answer is not A.
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Is quadrilateral MNPQ a rectangle? 23 Mar 2023, 09:20
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niyantg
Hello Bunuel

I have a doubt here.
If all 4 angles are 90 degrees then it can be a square also.

We dont know whether all 4 sides or only 2 sides opposite sides are equal ?

So should B be the answer ?
Please correct me

Thankyou.

All squares are rectangles so if MNPQ is a square it's a rectangle too.


Hi, can we really say all squares are rectangles ? Can you clarify some properties similar to this. I heard something similar about a square being a rhombus too ? Not sure how to understand this.

Example: I have another similar question below:

Is Quadrilateral a square?
(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrrilateral are equal in length.

OA: C

(1) Three angles of a quadrilateral are 90 degrees each: Then the quadrilateral can be a rectangle or a square.
(2) 3 sides of a quadrrilateral are equal in length: Then the quadrilateral can be a rhombus or a square.
(1) + (2): The quadrilateral has to be a square.

Here, point A says the same thing. However, the answer is not A.
Show more

A square is a quadrilateral (a four-sided polygon) in which all four sides are of equal length, and all four angles are right angles (90 degrees).

A rectangle is a quadrilateral in which opposite sides are parallel and equal in length, and all four angles are right angles. Unlike a square, a rectangle does not require all four sides to be of equal length.

Therefore, since a square meets all the criteria for a rectangle, it is considered a special case of a rectangle. However, not all rectangles are squares because a rectangle does not have to have four equal sides. A rectangle with sides of different lengths is not considered a square because it does not meet the definition of a square.

In summary, all squares are rectangles because they meet the criteria for a rectangle, but not all rectangles are squares because they do not meet the specific criteria of a square.

Check our collection of Properties of Polygons Questions. If you are looking to improve your geometry skills, this post is an excellent resource for anyone looking to master the properties of polygons.
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