Four-sided Figures: Types and Properties

FOUR-SIDED FIGURES

This lesson covers the following four-sided figures:

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

1. Rectangles

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

2. Squares

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

3. Parallelograms

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

4. Rhombuses

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

5. Trapeziums

trapezium
A trapezium has:
  • one pair of parallel sides

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?

opposite angles of a parallelogram
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).

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?

opposite angles of a parallelogram
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,
∠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°