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

Given quadrilateral ABCD,
In ∆ABC and ∆ABD,
AC = AD (Given)
∠CAB = ∠DAB (AB bisects ∠A)
AB = AB (Common)
∴ ∆ABC ≅ ∆ABD (By SAS congruence rule)
∴ BC = BD (By corresponding parts of congruent triangles are equal (CPCT))
∴ BC and BD are of equal lengths.