Question

In ΔABC, m∠B=90 and BE is a median. Prove that AB²+BC²+AC²=8BE².

Answer 1

SOLUTION IS IN THE ATTACHMENT..

PYTHAGORAS THEOREM : This theorem is also known as Baudhayan theorem.

This theorem states that : In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In ∆ ABC , ∠B = 90°

AC² = AB² + BC²

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Let, the vertices of the triangle A (0,b) B (0,0) and C(a,0).

BE is median hence E is the mid point of AC

So, E can be given as (a/2,b/2)

We, know if (p,q) and (r,s) are two point in coordinate space then distance between them given as $\sqrt{(r-p)^{2} + (s-q)^{2}}$.

Now ,apply formula in the above coordinate and proceed as given below.