Given that, in the figure AD⊥CD and CB⊥CD. AQ = BP and DP = CQ
We have to prove that ∠DAQ=∠CBP
Now, consider triangle DAQ and CBP,
We have
So, by RHS congruence criterion,
we have ΔDAQ≅ΔCBP
Now,
∠DAQ=∠CBP [∵ Corresponding parts of congruent triangles are equal]
∴ Hence proved