Properties of Quadrilaterals

Properties of Quadrilaterals

GCSE(F),

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.

Rectangle
All four interior angles are right angles
Square
A rectangle with all sides of equal length
Parallelogram
Two sets of parallel sides
Rhombus
A parallelogram with equal length sides
Kite
A quadrilateral reflected in the line BD
Trapezium
One set of parallel sides
DAB + CDA = 180º
ABC + BCD = 180º
trapezium properties

Examples

1. Give one difference between a trapezium and a parallelogram.

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

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

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

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Answer: 60º

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