Question

acbd is a quadrilateral AC is equal to AD and AB bisects Angle B then show that triangle ABC is congruent to triangle ABD

Answer 1

In triangles ABC and ABD
AC=AD(given)
Angle b/2= angle b/2(since AB bisects it)
AB=AB (common side)
Therefore triangles ABC and ABD are congruent (SAS axiom)

Answer 2

In △ ABC and △ ABD

AC = AD ( Given )

CAB = DAB ( AB Bisect A )

AB = AB ( Common )

△ ABC ≅ △ ABD ( SAS )