Question

Match the two columns.

Column 1	Column 2
A parallelogram is a rectangle if and only. if its diagonals are...	bisect each other.
The diagonals of a parallelogram.	parallel to the third
The line joining the mid-points of two sides of a triangle is	the third side
The line is drawn through the mid-point of one side of a triangle parallel to the other bisects	equal

Answer 1

Part A: A parallelogram is a rectangle if and only. if its diagonals are...

1. A parallelogram with one right angle is a rectangle. A quadrilateral whose diagonals are equal and bisect each other is a rectangle.
2. A parallelogram is a rectangle if and only if its diagonals are equals.

Thus, (A) - (IV)

Part B : The diagonals of a parallelogram.

1. A parallelogram is a quadrilateral whose opposite sides are parallel and equal.
2. The opposite sides being parallel and equal, forms equal angles on the opposite sides.
3. The diagonals of a parallelogram bisect each other.

Thus, (B) - (I)

Part C: The line joining the mid-points of two sides of a triangle is

The line joining the mid–points of two sides of a triangle is parallel to the third side.
This can be concluded form the mid–point theorem.

Thus, (C) - (III)

Part D: The line drawn through the mid-point of one side of a triangle parallel to the other bisects

The line is drawn through the mid–point of one side of a triangle parallel to the other and bisects the third side.

Thus, (D) - (II)