In a quadrilateral ACBC, AC = AD and AB bisect $∠ A$ . Show that $△ A B C$ is congruent to $△ A B D$ .

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Solution

In triangles $A B C$ and $A B D$ , we have

$A C = A D$ ........ (given);

$∠ C A B = ∠ D A B$ ......... $(∵ A B bisects ∠ A)$

$A B = A B$ ....... (common side).

Hence, by $S.A.S$ criterion

$△ A B C ≅ △ A B D$ . $[h e n c e p r o v e d]$

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