Question

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

Answer 1

Let us join AD.

In ΔABD and ΔACD,

AB = AC (Given)

BD = CD (Given)

AD = AD (Common side)

∴ ΔABD ΔACD (By SSS congruence rule)

⇒ ∠ABD = ∠ACD (By CPCT)