Read the statements carefully and state 'T' for true and 'F' for false.
(i) The line segment joining the mid-points of any two sides of a triangle is equal to third side.
(ii) Sum of adjacent angles of a parallelogram is 180^(@)`
(iii) If each pair of opposite angles of a quadrilateral are equal, then it is a parallelogram.

Options

A. (i)-T, (ii)-F, (iii)- T
B. (i)-F, (ii)-F, (iii)-T
C. (i)-F, (ii)-T (iii)-T
D. (i)-T, (ii)-T, (iii)-F

Answer

To solve the question, we will evaluate each statement one by one and determine if they are true (T) or false (F).

### Step-by-Step Solution:

1. **Evaluate Statement (i):**
- The statement says, "The line segment joining the mid-points of any two sides of a triangle is equal to the third side."
- Let's consider a triangle ABC. Let P be the midpoint of side AB and Q be the midpoint of side AC.
- The line segment PQ connects the midpoints of sides AB and AC. According to the Midpoint Theorem, PQ is parallel to side BC and is half its length, i.e., PQ = 1/2 BC.
- Therefore, the statement is **False (F)**.

2. **Evaluate Statement (ii):**
- The statement says, "Sum of adjacent angles of a parallelogram is 180°."
- In a parallelogram, opposite angles are equal, and the sum of all angles in any quadrilateral is 360°.
- If we denote the adjacent angles as x and y, we have: x + y + x + y = 360°, which simplifies to 2x + 2y = 360° or x + y = 180°.
- Thus, the statement is **True (T)**.

3. **Evaluate Statement (iii):**
- The statement says, "If each pair of opposite angles of a quadrilateral are equal, then it is a parallelogram."
- For a quadrilateral to be a parallelogram, one of the conditions is that both pairs of opposite angles must be equal.
- If angle A = angle C and angle B = angle D, then by the properties of quadrilaterals, the figure must be a parallelogram.
- Therefore, this statement is also **True (T)**.

### Final Answers:
- (i) F
- (ii) T
- (iii) T