Construct a trapezium ABCD, in which $A D ∥ B C$ and AD = 3.0 cm, AB = 2.5 cm, BC = 5.0 cm and CD = 2.8 cm. [4 MARKS]

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Solution

Concept : 1 Mark
Steps : 1 Mark
Construction : 2 Marks

Concept :
In trapezium ABCD, $A D ∥ B C$ . A trapezium can be divided into a parallelogram ABED and a triangle DEC.
AB = DE [Opposite sides of a parallelogram]

Steps of construction :

1. Construct a line segment of BC.
2. Divide BC into two parts as BE = 3cm and EC = 2cm.
3. Taking B as the centre, draw an arc of 2.5cm.
4. Taking E as the centre, draw an arc of 2.5cm which intersects the previous arc at point A.
5. Taking A as the center, draw an arc of 3cm.
6. Taking E as the center, draw an arc of 2.5cm which intersects the previous arc at point D.
7. Join AD and CD.
8. ABCD is your required trapezium.

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