Q) In the given figure, Δ ABC and ΔDBC are on the same base BC. If AD intersects BC at O, prove that

Ans: Let’s draw perpendicular from points A and D on line BC:

In Δ AON and Δ DOM,

∠ AON = ∠ DOM (interior angles)

∠ ANO = ∠ DMO (given that AN and DM are to BC)

  Δ AON Δ DOM

Hence, ………….. (i)

Now let’s calculate, :

=

=

by substituting values from equation (i), we get:

Hence proved.