Maths-

General

Easy

Question

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

Hint:

### From the information provided in the figure, find out the congruence rule used

and then prove the angles are equal.

## 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)

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