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Question Video: Completing a Sentence About Special Cases of Parallelograms Mathematics

A parallelogram whose _ are equal in length is called a rectangle.

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Video Transcript

A parallelogram whose what are equal in length is called a rectangle.

We can recall that a rectangle is a type of parallelogram with four congruent angles. The angles are all 90 degrees. We can sketch an example of a rectangle and consider that in fact there is something which we know is equal in length. The opposite sides in a rectangle are equal in length. However, if we consider the statement, we know that all parallelograms have opposite sides which are equal in length. Therefore, we’re looking for some additional property of rectangles which distinguish those from just any parallelogram. That property comes from the diagonals. The diagonals of a rectangle are equal in length.

Note that in general the only diagonal property of a parallelogram is that the diagonals of a parallelogram bisect each other. Therefore, if we have got a parallelogram and the diagonals are of equal length, then we know that it must be a rectangle. We can therefore complete the statement with the word diagonals. A parallelogram whose diagonals are equal in length is called a rectangle.

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