If all four interior angles of quadrilateral P have the same measure, which of the following statements must be true?

1. All sides of P have equal length.
2. The diagonals of P are perpendicular.
3. The measure of each interior angle of P is 90 degrees.

Thanks in advance!

Question

If all four interior angles of quadrilateral P have the same measure, which of the following statements must be true?

1. All sides of P have equal length.
2. The diagonals of P are perpendicular.
3. The measure of each interior angle of P is 90 degrees.

Thanks in advance!

anonymous · Answer

What do the interior angel of a quadrilateral add up to? If they all have equal measure, the answer should be pretty obvious.

anonymous · Answer

Well, I know that statement three is correct because of the sum of interior angles in the quadrilateral, but how can I prove the other two statements to be right/ wrong?

anonymous · Answer

Try coming up with some counter examples :) for example, can you think of a quadrilateral that has four right angles, and the sides arent equal?

anonymous · Answer

What does perpendicular mean? The definition of perpendicular is essentially the same thing as statement three.

anonymous · Answer

Ok.  The angles of a quadrilateral will always add up to 360 degrees.  Since we know all four angles are the same, 4(angle) = 360.  Try simplifying that a little.  Does that help?

anonymous · Answer

A big thank you to everyone who helped! I totally get the problem now, had a little brain fart on the perpendicular part. Thank you thank you thank you (: