In quadrilateral $A C B D, A C = A D$ and $A B$ bisects $∠ C A D .$ Show that $△ A B C ≅ △ A B D$ . Can you say that $B C$ = $B D$ ?

True

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False

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Solution

The correct option is A True
In $△ A B C$ and $△ A B D,$
$∠ C A B = ∠ B A D$ [Given]
$A C = A D$ [Given]
$A B = A B$ [Common]

So, by $S A S$ rule of congruence,
$△ A B C ≅ △ A B D$

As corresponding sides in congruent triangles are equal so, $B C = B D .$

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