Question

In figure, AB = AC and ∠ABD = ∠ACD, then ΔBDC will be :

(A) Equilateral triangle

(B) Isosceles triangle

(C) Equiangular triangle

(D) Scalene triangle

Answer 1

Answer is (B) Isosceles triangle

From figure,

AB = AC (Given)

∠ABC = ∠ACB

and ∠ABD = ∠ACD (Given) …(ii)

Adding equations (i) and (ii),

∠ABC + ∠ABD = ∠ACB + ∠ACD

∠DBC = ∠DCB

BD = DC (Opposite sides of equal angles)

∴ ΔBDC will be an isosceles triangle.