Answer
Proof of (a)
Disagree with the ΔABD = ΔCBD by the SAS congruence postulate .
SAS congurence property
In this congurence property two sides and one angle of the two triangles are equal .
(1) BD = BD ( Common sides of the ΔABD and ΔCBD )
(2) AB =BC (B is the midpoint of the AC i.e it bisect AC in the two equal parts.)
but equal angles are not given
therefore disagree with the ΔABD = ΔCBD by the SAS congurence postulate .
Proof of (b)
SSS congurence property
In this congurence property three sides of the two triangles are equal .
In the ΔABD and ΔCBD .
(1) BD = BD ( Common sides of the ΔABD and ΔCBD )
(2) AB =BC (B is the midpoint of the AC i.e it bisect AC in the two equal parts.)
(3) AD=CD (Given )
ΔABD = ΔCBD by the SSS congurence theorem
Hence proved
