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

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

Prove that the median of Delta ABC divides it into two triangles of equal area. .

You have studied in Class IX, (Chapter 9, Example 3), that a median of a triangle divides it into two triangles of equal areas. Verify this result for Delta ABC whose vertices are A(4, -6), B(3, -2) and C(5, 2).

If the diagonals of a parallelogram are equal, show that it is a rectangle.

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

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

Show that the diagonals of a square are equal and bisect each other at right angles.

Show that the diagonals of a square are equal and bisect each other at right angles.

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (b) If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

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.