Question

Construct a ∆ABC in which AB = AC = 5.2 cm and ∠A = 120°. Draw AD ⊥ BC.

Answer 1

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw AB=5.2 cm}\\ \text{2}\text{. Draw ∠BAX=120°}\\ \text{3}\text{. With A as the centre, cut the ray AX at 5.3 cm at point C.}\\ \text{4}\text{. Join BC.}\\ \text{5}\text{. With A as the centre and any radius, draw an arc cutting BC at M and N}.\\ 6.\text{With M as the centre and the radius more than half of MN, draw an arc.}\\ \text{7}\text{. With N as the centre and the same radius as before, draw another arc cutting the previously drawn arc at P.}\\ 8.\mathrm{Join}\mathrm{AP}\mathrm{meeting}\mathrm{BC}\mathrm{at}\mathrm{D}.\end{array} \\ \therefore \mathrm{AD}\perp \mathrm{BC} \end{gathered}$$