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Properties of Quadrilaterals

Properties of Quadrilaterals

Quadrilaterals are shapes with four sides.

In the following diagrams the arrows indicate parallel lines; the marks on lines indicate lines that are bisected; angles with the same value have the same colour; filled angles are bisected by the diagonals.

All four interior angles are right angles Properties of a rectangle

A rectangle where all sides are of equal length Properties of a square

Two sets of parallel sides Properties of a parallelogram

A parallelogram with equal length sides Properties of a rhombus

A quadrilateral reflected in the line BD Properties of a kite

One set of parallel sides

DAB + CDA = 180º

ABC + BCD = 180º

Properties of a Trapezium

Example 1

Give one difference between a trapezium and a parallelogram.

Or the opposite angles on a parallelogram are equal, which is not true for a trapezium.

Answer: A parallelogram has two sets of parallel sides: a trapezium only has one set

Example 2

What is the size of the angle CDA in this kite?

Missing angles on a kite

The angle BCD, directly opposite DAB, is equal to that angle and is 100º.

There are 360º in a quadrilateral: 360 - 100 - 100 - 100 = 60º

Answer: 60º