Question

In the given figure, AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

Answer 1

Based on the △ AOD and △ BOC

From the figure we know that ∠ AOD and ∠ BOC are vertically opposite angles.

So we get

∠ AOD = ∠ BOC

We also know that

∠ DAO = ∠ CBO = 90^o

It is given that AD = BC

Therefore, by AAS congruence criterion we get

△ AOD ≅ △ BOC

So we get AO = BO (c. p. c. t)

Therefore, it is proved that CD bisects AB.

Comments

Thanks for your solution