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When Three Sides and Two Included Angles are Given

Let us construct a quadrilateral ABCD in which AB = 3.6 cm, ∠ABC = 80°,
BC = 4 cm, ∠BAD = 120°, and AD = 5 cm.

First, we draw a rough sketch of quadrilateral ABCD and write down its
dimensions as shown.

Steps of construction:

Step 1: Draw a line segment AB = 3.6 cm.

Step 2: Draw ∠ABX = 80°.
Step 3: With B as centre and radius equal to 4 cm, draw an arc cutting
BX at C.

Step 4: Draw ∠BAY = 120°.

Step 5: With A as centre and radius equal to 5 cm, draw an arc cutting
AY at D.

Step 6: Join CD.

Thus, ABCD is the required quadrilateral as drawn alongside.
When Four Sides and One Angle are Given

Let us construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3.4 cm,
CD = 4.5 cm, AD = 5 cm and ∠B = 80°.

First we draw a rough sketch of quadrilateral ABCD and write down its dimensions
as shown.

Steps of construction:
Step 1: Draw a line segment AB = 3.8 cm.

Step 2: Make ∠ABX = 80°.

Step 3: From B, cut off BC = 3.4 cm.
Step 4: With A as the centre and radius equal to 5 cm draw an arc.

Step 5: With C as the centre and radius equal to 4.5 cm, draw another arc,
cutting the previous arc at D.

Step 6: Join AD and CD.

Thus, ABCD is the required quadrilateral.

Construction of Special Types of Quadrilaterals

To draw a quadrilateral, we used 5 measurements. However, some special quadrilaterals can be
constructed with less than 5 measurements. These are parallelograms, rectangles, squares and

rhombus.

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