Prove analytically the following :
If two medians of a triangle are equal, then the triangle is isosceles.

If two medians of a triangle are equal, prove that the triangle is isosceles.

Prove analytically that the : medians of a triangle are concurrent.

Prove analytically that the altitudes of a triangle are concurrent.

The median of a triangle divides it into two

If altitudes from two vertices of a triangle to the opposite sides are equal prove that the triangle is isosceles.

Show that a median of a triangle divides it into two triangles of equal areas.

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.