devashish wrote:

D is a point on side AC of ΔABC. Is ΔABC is isosceles?

(1) The area of triangular region ABD is equal to the area of triangular region DBC.

(2) BD┴AC and AD = DC

Can someone please explain the answer?

Hi,

I think that the OA is wrong. It should be E.

Stmt 1: Insufficient. Equal areas of two sub-triangles formed does not gaurantee that it is an isoceles triangle.

Stmt 2: This statement means that BD is a perpendicular bisector of side AC. It divides AC in equal halves. i.e. the perpendicular bisector and Median co-incide. This doesnt prove that it is an Isoceles triangle as it can also be an Equilateral triangle.

Property of Equilateral and Isocele - The perpendicular bisector , the meadian and altitude drwan to a particular side all conicide i.e. all are same lines.

So we cannot conclude that it is an Isoceles triangle. It can also be an Equilateral triangle.

Ans -E

two equal sides. So equilateral triangle is special type of isosceles triangle.