Q. 94.3( 3 Votes )

# If the median to

Answer :

Given:- ΔABC, AD is median

To Prove:- If AD is perpendicular on base BC then ΔABC is isosceles Proof:- Let, A at Origin be position vector of B and C respectively

Therefore, Now position vector of D, mid-point of BC i.e divides BC in 1:1

Section formula of internal division: Theorem given below

Let A and B be two points with position vectors respectively, and c be a point dividing AB internally in the ration m:n. Then the position vector of c is given by Position vector of D is given by Now distance/length of BC = position vector of C-position vector of B Now, assume median AD is perpendicular at BC

Then by Dot Product     AC = AB

Thus two sides of ΔABC are equal

Hence ΔABC is isosceles triangle

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