Rectangle

Dependencies: Parallelogram, Angle. A derived definition: add to a parallelogram the condition that one interior angle is a right angle.

Definition

Let $ABCD$ be a parallelogram.

If one interior angle is a right angle, then the parallelogram is called a rectangle.

One right angle is enough: the other three follow from opposite angles being equal and adjacent angles being supplementary. Thus every angle of a rectangle is a right angle.

Remarks

• One right angle is enough. In a parallelogram, the opposite angle equals it and each adjacent angle supplements it, so all four are $90^\circ$.
• Equal diagonals. A rectangle's diagonals bisect each other, as in every parallelogram, and also have equal length (Rectangle: equal diagonals).
• A square is a special case. Add equal adjacent sides, making the rectangle also a rhombus, and the result is a square.
• Circumcircle. All four vertices are equidistant from the diagonals' intersection, so every rectangle has a circumcircle centered there.