Construction for Class 9

Constructing quadrilaterals involves a combination of basic geometric tools such as a ruler, protractor and compass. These constructions are fundamental to understanding the properties and relationships between different types of quadrilaterals. In this chapter, we will explore the step-by-step procedures for constructing some common quadrilaterals: parallelogram, rectangle, rhombus, square, trapezium and kite.

Construction of Parallelogram

Constructing a parallelogram involves creating a quadrilateral where the opposite sides are both equal in length and parallel.
Steps to construct a parallelogram using different parameters are explained below:

(i) Construct a parallelogram by considering the lengths of two adjacent sides and an angle between them.

Using a ruler and a compass only, construct a parallelogram ABCD in which AB = 6.5 cm, BC = 4.8 cm and ∠ABC = 60°. 

(ii) Construct a parallelogram by considering the lengths of two adjacent sides and a diagonal. 

Using a ruler and a compass only, construct a parallelogram ABCD in which AB = 6.5 cm, AD = 4.8 cm and BD = 5.7 cm. 

(iii) Construct a parallelogram by considering the length of a side and both diagonals.

Using a ruler and a compass only, construct a parallelogram ABCD in which AB = 6.5 cm, AC = 6.4 cm and BD = 5.8 cm.

(iv) Construct a parallelogram by considering the lengths of diagonals and the angle between them.

Using a ruler and a compass only, construct a parallelogram ABCD in which AC = 6.4 cm, BD = 5.8 cm and angle between them is 60°.

(v) Construct a parallelogram by considering the lengths of two adjacent sides and a height.

Using a ruler and a compass only, construct a parallelogram ABCD in which AB = 6.5 cm, BC = 4.8 cm and height of 4 cm.

(vi) Construct a parallelogram by considering the lengths of a side, a diagonal and a height.

Using a ruler and a compass only, construct a parallelogram ABCD in which AB = 6.5 cm, AC = 6.4 cm and height of 4 cm.

(vii) Construct a parallelogram by considering both of its heights and an angle between two sides.

Using a ruler and a compass only, construct a parallelogram ABCD in which the lengths of the heights are 4 cm and 5.5 cm, respectively and the angle between any two sides is 60°.

Construction of Rectangle

Constructing a rectangle involves creating a quadrilateral where the opposite sides are both equal in length and parallel. Each interior angle of a rectangle is equal to 90°.
Steps to construct a rectangle using different parameters are explained below:

(i) Construct a rectangle by considering the lengths of adjacent sides.

Using a ruler and a compass only, construct a rectangle ABCD in which AB = 6.5 cm and BC = 4 cm.

(ii) Construct a rectangle by considering the lengths of a side and a diagonal.

Using a ruler and a compass only, construct a rectangle ABCD in which AB = 6.5 cm and BD = 7.8 cm.

Construction of Rhombus

Constructing a rhombus involves creating a quadrilateral where all sides are equal in length and opposite sides are parallel. Diagonals bisect each other at right angles.
Steps to construct a rhombus using different parameters are explained below:

(i) Construct a rhombus by considering the length of a side and an angle between two adjacent sides.

Using a ruler and a compass only, construct a rhombus ABCD in which AB = 6.5 cm and ∠A = 60°. 

(ii) Construct a rhombus by considering the length of a side and a diagonal.

Using a ruler and a compass only, construct a rhombus ABCD in which AB = 6.5 cm and AC = 7.8 cm.

(iii) Construct a rhombus by considering the lengths of the diagonals.

Using a ruler and a compass only, construct a rhombus ABCD in which AC = 6.5 cm and BD = 7.8 cm. 

Construction of Square

Constructing a square involves creating a quadrilateral where all sides are equal in length and opposite sides are parallel. The diagonals of the square are equal and bisect each other at right angles. 

Steps to construct a square using different parameters are explained below:

(i) Construct a square by considering the length of a side.

Using a ruler and a compass only, construct a square ABCD in which AB = 6.5 cm.

(ii) Construct a square by considering the length of a diagonal.

Using a ruler and a compass only, construct a square ABCD in which AC = 7.8 cm.

Construction of Trapezium

Constructing a trapezium involves creating a quadrilateral where it has two parallel sides and two non-parallel sides.

Steps to a trapezium using different parameters are explained below:

(i) Construct a trapezium by considering the lengths of all sides.

Using a ruler and a compass only, construct a trapezium ABCD in which AB = 6.5 cm, BC = 4.5 cm, CD = 4.8 cm and DA = 4 cm.

Construction of Kite

Constructing a kite involves creating a quadrilateral with two pairs of adjacent sides that are equal in length and one pair of opposite angles that are congruent. 

Steps to a kite using different parameters are explained below:

(i) Construct a kite by considering the lengths of two adjacent sides and an angle between them.

Using a ruler and a compass only, construct a kite ABCD in which AB = 6.5 cm, DA  = 4.8 cm and ∠A = 120°.

(ii) Construct a kite by considering the lengths of two adjacent sides and a diagonal.

Using a ruler and a compass only, construct a kite ABCD in which AB = 6.5 cm, DA  = 4.8 cm and DB = 7.8 cm.