Converse of Mid Point Theorem

Q. Explain Mid point theorem.

Q. In a parallelogram ABCD, P and Q are mid-points of sides DA and DC respectively. If $\angle DAC={30}^{\circ }$, then find the values of x and y?
[2 MARKS]

Q. If in the trapezium ABCD given above, AB is half of DC and also parallel to DC, then which of the following statements are correct?

1. AD = 2OA
2. A is the mid point of OD
3. B is the mid point of CO
4. CB = 2BO

Q. If the line joining the mid points D and E of the sides AB and CA respectively is extended to point F such that
DE = EF, then which of the following statement(s) is/are correct?

1. DFCB is a parallelogram
2. DF = EC
3. EF is half of BC
4. AD = BC

Q. In $\Delta ABC,\angle A={45}^{\circ },\angle B={60}^{\circ }$, and $\angle C={75}^{\circ }$. Find the angles formed by joining the mid-points of the sides of the given triangle.

Q. Which of the following states that, "If a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side" ?

1. Basic proportionality theorem
2. Converse of midpoint theorem
3. Midpoint theorem
4. Pythagorean Theorem

Q. In $\Delta ABC,\angle A={45}^{\circ },\angle B={60}^{\circ }$, and $\angle C={75}^{\circ }$. Find the angles formed by joining the mid-points of the sides of the given triangle.