# Four-sided Figures: Types and Properties

### Types of four-sided figures

1. Rectangles
2. Squares
3. Parallelograms
4. Rhombuses
5. Trapeziums

### Rectangles

In a rectangle:
• opposite sides are parallel and equal
• all angles are 90°

### Squares

In a square:
• all sides are equal
• opposite sides are parallel
• all angles are 90°

### Parallelograms

Rectangles and squares are examples of parallelograms.
In a parallelogram:
• opposite sides are parallel and equal

### Rhombuses

A square is an example of a rhombus.
In a rhombus:
• all sides are equal
• opposite sides are parallel

### Trapeziums

A trapezium has:
• one pair of parallel sides

### 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

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°