## Four-sided Figures: Types and Properties

#### FOUR-SIDED FIGURES

This lesson covers the following four-sided figures:

#### 1. Rectangles

In a rectangle:

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

#### 2. Squares

In a square:

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

#### 3. Parallelograms

In a parallelogram:

- opposite sides are parallel and equal

Rectangles and squares are examples of parallelograms.

#### 4. Rhombuses

In a rhombus:

- all sides are equal
- opposite sides are parallel

A square is an example of a rhombus.

#### 6. 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

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.

∠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).

∠b = ∠d

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

#### 7. 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?

In our case,

∠a = 110°

∠b = 130°

∠c = 50°

∠d = 70°

Therefore,

∠a + ∠d = 110° + 70° = 180°

∠b + ∠c = 130° + 50° = 180°

In our case,

∠a = 110°

∠b = 130°

∠c = 50°

∠d = 70°

Therefore,

∠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,

Also, AD // BC

So,

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,

But, AD~~//~~ BC

So,

So,

**∠a + ∠d = 180°**, and**∠b + ∠c = 180°**But, AD

So,

**∠a + ∠b ≠ 180°**, and**∠d + ∠c ≠ 180°**