Types of Quadrilaterals
Grade 3The quadrilateral family
A quadrilateral is any four-sided polygon with an angle sum of 360°. There are six types you need to know well, and they overlap — a square is a special rectangle, which is a special parallelogram.
Square: all sides equal, all angles 90°, diagonals bisect at right angles. Rectangle: opposite sides equal, all angles 90°, diagonals equal. Parallelogram: opposite sides parallel and equal, opposite angles equal, diagonals bisect each other. Rhombus: all sides equal, opposite angles equal, diagonals bisect at right angles. Trapezium: exactly one pair of parallel sides. Kite: two pairs of adjacent equal sides, one diagonal is the axis of symmetry.
The properties to remember
Parallel sides, equal sides, equal angles, and diagonal properties — exam questions test each of these. Sketch the shape and mark on what you know; it makes the property much easier to spot.
Worked example
EXAMPLE
ABCD is a parallelogram. Angle A = 72°. Find angles B, C, and D.
In a parallelogram, opposite angles are equal: angle C = 72°. Adjacent angles are supplementary (co-interior angles, parallel sides): angle B = 180° − 72° = 108°. So angle D = 108° and angle B = 108°, angle C = 72°.
