Assertion (A): In the figure, if AD = DC = 4 cm, EC = 10 cm and DE || AB, then CE = 5 cm.

Reason (R): The straight line drawn through the mid-point of one side of a triangle parallel to other, bisects the third side.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Assertion (A): The mid-points of the sides of a quadrilateral ABCD are joined in order to get quadrilateral PQRS. PQRS is a rhombus.

Reason (R): Adjacent sides of a rhombus are equal and perpendicular to each other.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

D and E are the mid-points of the sides AB and AC respectively of △ABC. DE is produced to F. To show that CF is equal and parallel to DA, we need an additional information, which is :

1. DE = EF

2. AE = EF

3. ∠DAE = ∠EFC

4. ∠ADE = ∠ECF

In which of the following cases you will get 2XY = QR for the given figure?

(i) When PX = QX and PY = RY

(ii) When PX = QX and a + b = 180°

1. Only in case (i)

2. Only in case (ii)

3. In both the cases

4. None of these