Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Show that the diagonals of a rhombus divide it four congruent triangles.

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

Show that the bisectors of angles of a parallelogram form a rectangle.

Using vector method, prove that if the diagonals of a parallelogram are equal, then it is a rectangle.

Prove that the sum of the squares of the squares of tha diagonals of a parallelogram is equal to tha sum of the squares of its sides.

Show that the diagonals of a square are equal and right bisectors of each other.

Verify the Median of a triangle divides into two triangles of the equal whose vertices are A(4,-6),B(3,-2) and C(5,2)

Using vectors prove that the diagonals of a parallelogram bisect each other.