in the given figure, ab=ac, d is the point in the interior of triangle abc such that angle dbc=angle dcb. prove that ad bisects angle bac of triangle abc

Question

in the given figure, ab=ac, d is the point in the interior of
triangle abc such that angle dbc=angle dcb prove that ad bisects
angle bac of triangle abc

Madhumathi Govind · Accepted Answer

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
Hope i cud help ya =D
Madhumathi