Question

On his math test Balaban wrote that a four sided polygon that has at least two right angles must be a rectangle or a square. Dana wrote that a four Sided polygon needs at least three right angles to be a rectangle or a square. Who is right

Answer 1

Dana is correct. The sum of the angles in a quadrilateral is 360°, so if 3 of the angles are 90°, the fourth must also be 90°, creating a rectangle or a square.

Answer 2

The statement given by Dana is correct. We need at least 3 right angles in a polygon for it being a rectangle or square.

What is the sum of interior angles of four sided polygon?

If a polygon is four sided (a quadrilateral), the sum of its angles is 360°

If we know that three angles are of 90 degrees (right angle), then the fourth angle would also have to be of 90 degree so that all those four angles together sum up to make 360 degree.

So if we know that three angles are right angled in a four sided polygon, then it is a rectangle or a square.

Now, see the figure attached below. Its a four sided polygon with two angles as right angles, but still its not a square.

So there exists a counter example for statement given by Balaban.

Two angle being a right angle is also not sufficient, nor a single angle being right angle is sufficient.
So we need at least 3 angles to be right angle for that quadrilateral being a rectangle or square.

Thus, the statement given by Dana is correct. We need at least 3 right angles in a polygon for it being a rectangle or square.

Learn more about quadrilaterals here:

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