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