Prove that the sum of the vectors directed from the vertices to the mid-points of opposite sides of a triangle is zero.

Prove that the sum of three altitudes drawn from the vertices to opposite sides of a triangle is less than the sum of three sides. or Prove that the perimeter of a triangle is greater than the sum of three altitudes drawn from the vertices to opposite of a triangle.

Medians the line segments joining the vertices to the mid-points of the opposite side of a triangle are known as its medians.

Prove that the perpendicular from the vertices to the opposite sides (i.e. Altitudes) of a triangle concurrent.

Prove that the line joining the mid-points of the two sides of a triangle is parallel to the third side.

Prove that the line joining the mid-points of the two sides of a triangle is parallel to the third side.

Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.