Question

ABCD is a quadrilateral in which AB=BC and AD =CD ,Show that BD bisects both the angles ABC and ADC {by using SAS congruence }

Answer 1

You can't use SAS, since you know nothing about any of the angles
BUT, you can use SSS to prove
∆ ABD congruent to ∆ CBD

Therefore corresponding angles are equal, that is
∠ABD = ∠CBD and ∠ADB = ∠CDB by SSS

Answer 2

oops sorry

angle abd=angle1
angle adb=angle 3
angle cbd=angle 2
angle bdc=angle 4

Answer 3

In ∆ABD, we know that AB=AD, so ∡D=∡B
Since BD bisects ∡ADC, in BDC, ∡B=∡D, so DC=BC. Since the two triangles share side BD, they are congruent by ASA or SAS