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Question We saw that one of the properties of a rectangle is that its opposite sides are parallel. Can this be chosen as a definition of a rectangle? In other words, is every quadrilateral that has opposite sides parallel and equal a rectangle?
Let ABCD be a quadrilateral in which opposite sides are parallel and equal. Here AB || DC and AD || BC. Also, AB = DC and AD = BC. In the quadrilateral ABCD, opposite sides are equal. For ABCD to be a rectangle, we require each angle to be 90°. Given information AB || DC and AD || BC can not help us to prove that each angle of ABCD is 90°. ∴ ABCD may not be a rectangle. ∴ A rectangle can not be defined as a quadrilateral with equal and parallel opposite sides. 4.2 Angles in a Quadrilateral, 4.3 More Quadrilaterals with Parallel Opposite Sides, 4.4 Quadrilaterals with Equal Sidelengths Figure It Out (Page 102)