D and E are mid-points of the sides AB and AC of △ABC and O is any point on the side BC. O is joined to A. If P and Q are mid-points of OB and OC respectively, then DEQP is

1. a square

2. a rectangle

3. a rhombus

4. a parallelogram

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 figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only if

1. ABCD is a rhombus

2. diagonals of ABCD are equal

3. diagonals of ABCD are perpendicular to each other

4. diagonals of ABCD are equal and 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.