If D is any point on the side BC of $Δ A B C$ such that $Δ A D B$ and $Δ A D C$ 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
Consider the $△ A B C$ .
It is given that
$∠ A D E = ∠ A D C$
This means that $A D$ is the median.
i.e. median divides the triangle into two equal parts.

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If D is any point on the side BC of ΔABC such that ΔADB and ΔADC are equal in area, then

The correct option is A AD is the medianConsider the △ABC.It is given that∠ADE=∠ADCThis means that AD is the median.i.e. median divides the triangle into two equal parts.

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

The correct option is A AD is the median
Consider the $△ A B C$ .
It is given that
$∠ A D E = ∠ A D C$
This means that $A D$ is the median.
i.e. median divides the triangle into two equal parts.