Question

Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ∠ABC = 120°.

Answer 1

Steps of construction:
Step 1: Draw AB= $3.5\mathrm{cm}$.
Step 2: Make $\angle ABC={120}^{\circ }$.
Step 3: With B as the centre, draw an arc $3.5\mathrm{cm}$ and name that point C.
Step 4: With C as the centre, draw an arc $5.2\mathrm{cm}$.
Step 5: With A as the centre, draw another arc ​$5.2\mathrm{cm}$, cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, $ABCD$ is the required quadrilateral.