Question

# What is the relation between ∠1 and ∠2 if AD = CD?

- ∠1 > ∠2
- ∠1 < ∠2
- ∠1 = ∠2
- ∠1 = ∠2

Hint:

### ΔABD ≅ ΔCBD (RHS congruence criterion)

## The correct answer is: ∠1 = ∠2

From figure, in ΔABD and ΔBCD,

∠BAD = ∠BCD = 90°

AQ = CD (given)

BD = BD (common side)

⇒ ΔABD ≅ ΔCBD (RHS congruence criterion)

⇒∠1 = ∠2 (Corresponding parts of congruent triangles)

∠BAD = ∠BCD = 90°

AQ = CD (given)

BD = BD (common side)

⇒ ΔABD ≅ ΔCBD (RHS congruence criterion)

⇒∠1 = ∠2 (Corresponding parts of congruent triangles)

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