X is a point on median AL of triangle ABC. Prove that triangle ABX is equal in area.

P is a point on the median AD of the triangle ABC.Prove that triangle APB = triangle APC.

AD is a median of triangle ABC. Prove that : AB+AC gt 2AD

P is a point on the median AD of the Delta ABC . Prove that area of Delta APB = area of Delta APC .

If A(4,-6),B(3,-2) and C(5,2) are the vertices of $ABC, then verify the fact that a median of a triangle ABC divides it into two triangles of equal areas.

Consider the following statements : 1. Let D be a point on the side BC of a triangle ABC: If area of triangle ABD = area of triangle ACD, then for all points O on AD, area of triangle ABO = area of triangle ACO. 2. If G is the point of concurrence of the medians of a triangle ABC, then area of triangle ABG = area of triangle BCO = area of triangle ACG. Which of the above statements is/are correct?

If G is the centroid of triangle ABC , prove that area triangle AGB = 1/3 area triangle ABC .

G is the centroid of the triangle ABC. Prove that the area of the triangle ABG is one third of the area of the triangle ABC.

In the following figures, the sides AB and BC and the median AD of triangle ABC are respectively equal to the sides PQ and QR and median PS of the triangle PQR. Prove that Delta ABC and Delta PQR are congruent.

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