Given :- $A C = A D$
$∠ C A B = ∠ B A D$
To prove :- $△ A B C ≅ △ A B D$
Proof :- $9 n △ A B C$ & $△ A B D$
$A C = A D$
$∠ C A B = ∠ B A D$
$A B = B A$
$△ A B C ≅ △ A B D$
$B C = B D$

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Solution

$\begin{matrix} G i v e n ∠ C A B = ∠ B A D I n Δ C A B a n d D A B A B = A B (c o m m o n) ∠ C A B = ∠ D A B (g i v e n) A C = A D (g i v e n) B y S . A . S . c o n g r u e n c y Δ C A B ≅ D A B ∴ B C = B D \end{matrix}$

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