The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle if

1. PQRS is a parallelogram

2. PQRS is a rectangle

3. the diagonals of PQRS are perpendicular to each other

4. the diagonals of PQRS are equal.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order is a rhombus if

1. ABCD is a parallelogram

2. ABCD is a rhombus

3. the diagonals of ABCD are equal

4. the diagonals of ABCD are perpendicular to each other.

Consider the following two statements:

Statement 1: The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.

Statement 2: The line through the mid-point of one side of a triangle and parallel to another side bisects the third side.

Which of the following is valid?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and Statement 2 is false.

4. Statement 1 is false, and Statement 2 is true.

Assertion (A): For a Δ ABC, line segment EF is drawn such that E is the midpoint of AB and F is a midpoint of AC. Then the quadrilateral formed EFCB is a trapezium.

Reason (R): The line segment joining the midpoint of two sides of a triangle is parallel to the third side.

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).