#### Question

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

#### Solution

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)

Is there an error in this question or solution?

Solution ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD. Concept: Properties of a Triangle.