In ΔABD, AB = AD and AC is perpendicular to BD. State the congruence rule by

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In $Δ A B D$ , AB = AD and AC is perpendicular to BD. State the congruence rule by which $Δ A C B ≅ Δ A C D$ .

Options:

A . SAS congruence rule

B . SSS congruence rule

C . RHS congruence rule

D . ASA congruence rule

Answer: Option C
:
C

$In the given triangle, A B = A D (Given) A C is the common side ∠ A C B = ∠ A C D = 90^{\circ}$
$∴ Δ A C B ≅ Δ A C D$ [ RHS criteria]
Hence, by RHS congruence rule, the two triangles are congruent.

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