Consider the following statements relating to the congruency of two right triangles.
(1) Equality of two sides of one triangle with any two sides of the second makes the triangle congruent.
(2) Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangle congruent.
(3) Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangle congruent.
Of these statements :

Options

A. 1, 2 and 3 are correct
B. 1 and 2 are correct
C. 1 and 3 are correct
D. 2 and 3 are correct

Answer

To determine the validity of the statements relating to the congruency of two right triangles, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Analyzing Statement 1:**
- Statement: "Equality of two sides of one triangle with any two sides of the second makes the triangle congruent."
- Explanation: In triangle congruency, we need to follow specific rules. The Side-Side-Side (SSS) and Side-Angle-Side (SAS) criteria are used for congruency. However, just having two sides equal does not guarantee congruency unless the included angle is also equal.
- Conclusion: **This statement is false.**

2. **Analyzing Statement 2:**
- Statement: "Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangle congruent."
- Explanation: This follows the Right Angle-Hypotenuse-Side (RHS) congruency criterion. If the hypotenuse and one corresponding side of two right triangles are equal, then the triangles are congruent.
- Conclusion: **This statement is true.**

3. **Analyzing Statement 3:**
- Statement: "Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangle congruent."
- Explanation: This follows the Angle-Angle-Side (AAS) criterion. In a right triangle, if the hypotenuse and one acute angle are equal to the hypotenuse and one angle of another triangle, the triangles are congruent.
- Conclusion: **This statement is true.**

### Final Conclusion:
- Statement 1 is false.
- Statement 2 is true.
- Statement 3 is true.

Thus, the correct option includes statements 2 and 3 as true.