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?
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.
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