Answer to the 36th question "DON'T SEND STHE SIMILAR QUERIES KINDLY PERFORM THE STEP BY STEP AND APPROPRIATE ANSWER" - Maths - Congruency of Triangles

Question

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

Ayushi Chaurasiya · 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
Regards

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.

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.