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

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

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Given that AC = AD 

∠BAC = ∠BAD (∵ AB bisects ∠A)

Now in ΔABC and ΔABD 

AC = AD (∵ given) 

∠BAC = ∠BAD (Y given) 

AB = AB (common side) 

∴ ΔABC ≅ ΔABD 

(∵ SAS congruence rule)

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