There are different types of quadrilaterals; these quadrilaterals are classified by the relationship of their sides, angles and diagonals.

If we are given the dimensions of the sides, diagonals and  measurement of angles we may be able to visualize and construct these quadrilaterals. Some of the quadrilaterals that we should practice constructing are parallelogram, rhombus, square and many other quadrilaterals with varying angles.

Let us understand their construction with few simple examples .

1) Construct a parallelogram ABCD in which AB = 12 cm, BC = 9 cm and diagonal AC = 13.6 cm.

Solution:

To start with roughly draw the required parallelogram and write down the given dimensions.

Steps of Construction:

(i) Draw AB = 12 cm.
(ii) With A as center and radius 13.6 cm, draw an arc.
(iii) With B as center and radius 9 cm draw another arc, cutting the previous arc at C.
(iv) Join BC and AC.
(v) With A as center and radius 9 cm, draw an arc.
(vi) With C as center and radius 12 cm draw another arc, cutting the previously drawn arc at D.S
(vii) Join DA and DC.

Then, ABCD is the required parallelogram.

2) Construct a square ABCD, each of whose diagonals is 10.4 cm.

Solution:

We know that the diagonals of a square bisect each other at right angles.

Steps of Construction:

(i) Draw the right bisector XY of pr, meeting pr at O.
(ii) From O set off Oq = 1/2 (10.4) = 5.2 cm along OY and Os = 5.2 cm along OX.
(iii) Join pq,qr,rs,and ps

Then, ABCD is the required square.

Draw pr = 10.4 cm.

3) Construct a rhombus with side 4.2 cm and one of its angles equal to 65°.

Solution:

Clearly, the adjacent angle = (180° - 65°) = 115°. So, we may proceed according to the steps given below.

Steps of Construction:

(i) Draw BC = 4.2 cm.
(ii) Make ∠CBX = 115° and ∠BCY = 65°.
(iii) Set off BA = 4.2 cm along BX and CD = 4.2 cm along CY.