Question

In the figure ABC and DBC are two isosceles triangle on the same base BC. SHOW THAT <ABD =< ACD

Answer 1

angABC = angACB. ------(1)
angDBC = angDCB --------(2)
thus, adding (1) and (2) gives the required result.

Answer 2

GIVEN THAT ABC AND DBC ARE ISOSCELES THEN, IN ABC AB=AC
AND IN DBC, DB=DC
AND WE KNOW THAT ANGLES OPP. TO EQUAL SIDES ARE EQUAL
. <ABC=<ACB AND <DBC=<DCB
ADDING THESE
<ABD=<ACD