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°