PS set:

[thumpin_termis]

In the figure above, D is a point on the side AC of triangle ABC. Is triangle ABC an isosceles?

(1) The area of triangle region ABD is equal to the area of triangular region DBC.
(2) BD is perpendicular to AC, and AD = DC.

.
.
.
.
.
.
.
.
.

The answer is B.

I'm just a bit confused with statement 2. I see that in this case, the triangle will be _at least_ a isosceles, but what if triangle ABC is an equilateral triangle? Would this still be a valid answer then?

[givemeanid]

Equilateral triangle is just a special case of an isosceles triangle. Every equilateral triangle is an isosceles triangle but not vice-versa.

So, (B) is sufficient.