Question

ABC and DBC are two isosceles triangles on the same base BC (see Fig). Show that ∠ABD = ∠ACD.

Answer 1

Let us join AD.

In ∆ABD and ∆ACD,

AB = AC (Given)

BD = CD (Given)

AD = AD (Common side)

∠∆ABD ≅ ∠∆ACD (By SSS congruence rule)

∠ABD = ∠ACD (By CPCT)