If D is any point on the side BC of $△ A B C$ such that $△ A D B$ and $△ A D C$ are equal in area, then

AD is the median

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AD is the altitude

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AD is an angle bisector

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AD is any line

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Solution

The correct option is A AD is the median
$I f D i s a n y p o i n t o n t h e s i d e B C o f △ A B C s u c h t h a t △ A D B a n d △ A D C a r e$
$e q u a l i n a r e a, t h e n A D i s t h e m e d i a n$
AD divides both the triangles in equal areas. so it is the median.
As we know a median of a triangle is the line segment from a vertex of a triangle to the mid point of the side opposite to the vertex.

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