If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that 

The correct answer is: congruent triangles

AD ⊥ CD (given)
and BC ⊥ CD (given)
AQ = BP and DP = CQ (given)
To prove : ∠ DAQ = ∠ CBP
AD ⊥ CD (given)
and BC ⊥ CD (given)
∴ ∠ D = ∠ C (each 90°)
∵ DP = CQ (given)
On adding PQ to both sides. we get
DP + PQ = PQ + CQ…(i)
⇒ DQ = CP
Now, in right angles ADQ and BCP
∴ AQ = BP (hypotenuse)
DQ = CP (from (i))
∴ Δ ADQ ≡ Δ BCP (Right angle hypotenuse side (RHS congruence rule))
∴ ∠ DAQ = ∠CBP (Corresponding part of congruent triangles)