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
Let perpendicular distance of side BC from the vertex A be h ,
Area of $△ A D B = \frac{1}{2} (D B \times h)$
Area of $△ A D C = \frac{1}{2} (D C \times h)$
But it is given that Area of $△ A D B =$ Area of $△ A D C$ ,
which gives DB = DC .
Therefore , AD is the median .

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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 medianLet perpendicular distance of side BC from the vertex A be h ,Area of △ADB=12(DB×h)Area of △ADC=12(DC×h)But it is given that Area of △ADB= Area of △ADC,which gives DB = DC .Therefore , AD is the median .

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