Which of the following statements is CORRECT ?
(i) If two geometric figures superimpose each other exactly when placed one over the other, then the figures are said to be congruent to each other.
(ii) If two sides and the included angle of one triangle are equal to corresponding sides and the included angle of another triangle, then the two triangles are congruent to each other by SAS (Side-Angle-Side) congruency.
(iii) If two angles and the included side of one triangle are equal to corresponding angles and the included side of another triangle, then the two triangles are congruent to each other by ASA (Angle-Side-Angle) congruency.

Options

A. Only (i)
B. Only (ii) and (iii)
C. Only (i) and (ii)
D. (i), (ii) and (iii)

Explanation

To determine which of the statements is correct, we will analyze each statement one by one.

### Step 1: Analyze Statement (i)
**Statement (i)**: If two geometric figures superimpose each other exactly when placed one over the other, then the figures are said to be congruent to each other.

**Analysis**: This statement is true. Two figures are considered congruent if they can be perfectly overlaid on each other, meaning they have the same shape and size.

### Step 2: Analyze Statement (ii)
**Statement (ii)**: If two sides and the included angle of one triangle are equal to corresponding sides and the included angle of another triangle, then the two triangles are congruent to each other by SAS (Side-Angle-Side) congruency.

**Analysis**: This statement is also true. The SAS criterion states that if two sides of one triangle are equal to two sides of another triangle, and the angle between those sides is equal, then the triangles are congruent.

### Step 3: Analyze Statement (iii)
**Statement (iii)**: If two angles and the included side of one triangle are equal to corresponding angles and the included side of another triangle, then the two triangles are congruent to each other by ASA (Angle-Side-Angle) congruency.

**Analysis**: This statement is true as well. The ASA criterion states that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the triangles are congruent.

### Conclusion
Since all three statements are correct, we conclude that the answer is that all statements (i), (ii), and (iii) are correct.

### Final Answer
All statements are correct.

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