In quadrilateral ABCD, AC = AD and AB bisects $∠$ A. Show that $△ A B C ≅ △ A B D$ . What can you say about BC and BD ?

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Solution

In $△ A B C a n d △ A B D$ ,
$A C = A D$
$∠ C A B = ∠ D A B$
$A B = A B$
So, by SAS congruence rule,
$△ A B C ≅ △ A B D$
$B C = B D$ [By CPCT]

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