Triangle BDC is isosceles. Which angle is congruent to BAD?
BCD, CAB, DBC, ACD

Solution:

The triangle BDC is an isosceles triangle and is located inside a circle.

Since the sides of the triangle BC and BD are congruent ie. equal.

BC = BD,

⇒ The sectors of the circle they travel along are congruent also.

Also for ΔBAC and ΔBAD,

AD=AC = Radius of circle

AB = BA ( common side)

Hence, ΔBAC is congruent to ΔBAD by SSS criteria.

Therefore, 

by cpct, ㄥBAD is congruent to ㄥBAC or ㄥCAB.

Triangle BDC is isosceles. Which angle is congruent to BAD?

Summary:

Given Triangle BDC is isosceles. By using congruency criteria ㄥBAD is congruent to ㄥBAC or ㄥCAB