# Four-sided Figures: Types and Properties

*Types of four-sided figures*

*Types of four-sided figures*

- Rectangles
- Squares
- Parallelograms
- Rhombuses
- Trapeziums

*Rectangles*

*Rectangles*

In a rectangle:

- opposite sides are parallel and equal
- all angles are 90°

*Squares*

*Squares*

In a square:

- all sides are equal
- opposite sides are parallel
- all angles are 90°

*Parallelograms*

*Parallelograms*

Rectangles and squares are examples of parallelograms.In a parallelogram:

- opposite sides are parallel and equal

*Rhombuses*

*Rhombuses*

A square is an example of a rhombus.In a rhombus:

- all sides are equal
- opposite sides are parallel

*Trapeziums*

*Trapeziums*

A trapezium has:

- one pair of parallel sides

*Opposite angles of a parallelogram*

*Opposite angles of a parallelogram*

Make a parallelogram or trapezium using a set square and a ruler, or trace one from your book. Now, measure its angles using a protractor. What do you notice?

In our case,

∠a = 60°

∠b = 120°

∠c = 60°

∠d = 120°

Therefore,

∠a = ∠c

∠b = ∠d

Conclusion:

∠a = ∠c

∠b = ∠d

The opposite angles of a parallelogram are equal.

∠a = ∠c

∠b = ∠d

The opposite angles of a rhombus are equal (as a rhombus is a type of parallelogram).

*Sum of a pair of angles between two parallel lines*

*Sum of a pair of angles between two parallel lines*

Make a parallelogram or trapezium using a set square and a ruler, or trace one from your book. Now, using a protractor, measure all the angles of the figure. What do you notice?

∠a = 110°

∠b = 130°

∠c = 50°

∠d = 70°

∠a + ∠d = 110° + 70° = 180°

∠b + ∠c = 130° + 50° = 180°

Conclusion:

The sum of a pair of angles between two parallel lines is 180°.

In a parallelogram, AB // DC. So,

∠a + ∠d = 180°, and∠b + ∠c = 180°

Also, AD // BC. So,

∠a + ∠b = 180°, and∠d + ∠c = 180°

In a trapezium, AB // DC. So,

∠a + ∠d = 180°, and∠b + ∠c = 180°

But, AD~~//~~BC. So,

∠a + ∠b ≠ 180°, and∠d + ∠c ≠ 180°