If D is any point on the side BC of Delta ABC such that Delta ADB and Delta ADC are equal in area- thenAD is the medianAD is the altitudeAD is an angle bisectorAD is any line

Question

Toppr Admin · Accepted Answer

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 .

If D is any point on the side BC of ΔABC such that ΔADB and ΔADC are equal in area, thenAD is the medianAD is the altitudeAD is an angle bisectorAD is any line

Let 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
AD is the median
AD is the altitude
AD is an angle bisector
AD is any line

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 .