In quadrilateral $A C B D$ , $A C = A D$ and $A B$ bisects $∠ A$ (see Fig). Show that $△ A B C ≅ △ A B D$ . What can you say about $B C$ and $B D$ ?

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Solution

$I n Δ A B C a n d Δ A B D$
$A C = A D (g i v e n)$
$∠ C A B = ∠ D A B (g i v e n)$
$A C = A B (c o m m o n)$
So, $Δ A B C ≅ Δ A B D (b y S A S c r i t e r i o n)$
Now, $Δ A B C ≅ Δ A B D$
$\Rightarrow B C = B D (b y c . p . c . t)$
Therefore $B C$ and $B D$ are equal

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In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?

∠ A

△ A B C ≅ △ A B D

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Δ A B C ≅ Δ A B D .

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