Answer to the 36th question."DON'T SEND STHE SIMILAR QUERIES.KINDLY PERFORM THE STEP BY STEP AND APPROPRIATE ANSWER".
Q.36. In the adjoining figure, AB = AC, D is a point in the interior of ABC such that DBC = DCB. Prove that AD bisects BAC of ABC.
draw a triangle abc with point d somewhere in the centre. join db, dc and da
B and C are the bases of ur triangle.... u should get a triangle dbc insode the original triangle abc
GIVEN: ab = ac, angle dbc = dcb
TO PROVE:AD bisects angle A
PROOF: given angle dbc = dcb
Therefore DB = DC [sides opp. equal angles of a triangle]
Consider Triangles ABD, ACD
AB = AC [given]
AD = AD [common]
DB = DC [proven]
Therefore triangle ABD congruent to triangle ACD by SSS cong. rule
By cpct, angle BAD = CAD
Therefore AD bisects angle BAC.