Lesson: Geometry - 22

Rectangles

[Page 25 of 30]

The rectangle, like the square, is one of the most commonly known quadrilaterals. It is defined as having all four interior angles 90° (right angles). The diagonals of a rectangle are congruent.

A rectangle is a parallelogram with:

  • four right angles
  • equal diagonals that bisect each other

If a quadrilateral has one of these two features, it will have the other one, and is a rectangle. Rectangles have equal opposite sides.

The perimeter of a rectangle is the sum of the sides. Since there are two equal lengths and two equal widths, the perimeter of a rectangle is 2l + 2w.

Interior angles of a quadrilateral must sum to 360°, so we know that ∠ S = 360° - 3(90°) = 90°. This means that the opposite sides of QRST are of equal length, so QR=TS, QT=RS, and QS=RT.

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