Types of Quadrilaterals

Grade 3

The 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°.

Try this one

The diagram shows quadrilateral PQRS. The interior angles are as shown.

(a) Show that \(y = 43\). [3]

(b) Hence find the size of angle \(PQR\). [1]

Nova's hint:

This question uses the angle sum of a quadrilateral.

Ask yourself: 'What do the four interior angles of any quadrilateral add up to?' Once you have that total, form an equation by adding all four expressions and solve for \(y\).

Try to Solve it with Nova?