Prove that each diagonal of a parallelogram divides it into two congruent triangles.

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

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

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

If the diagonals of a parallelogram are equals then show that it is a rectangle.

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

Prove that a cyclic parallelogram is a rectangle.

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

prove that the line segment joining the midpoints of two opposite sides of a parallelogram divides the parallelogram into two parallelograms with equal area.

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)

Statement 1: If | vec a+ vec b|=| vec a- vec b|,t h e n vec aa n d vec b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle.