Geometry

Question Analysis:
This question focuses on identifying the sufficient conditions for proving the congruence of two right - triangles using the HL (Hypotenuse - Leg) Theorem.
The main task is to match the given options with the requirements of the HL Theorem, which states that the hypotenuse and a leg of one right - triangle must be congruent to the hypotenuse and a leg of another right - triangle.

Key Concept Explanation:
The HL Theorem for right - triangles: If the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.
In right - triangle with right - angle , is the hypotenuse, and or are the legs.
Similarly, in with right - angle , is the hypotenuse, and or are the legs.

Step - by - Step Solution:
1. Analyze option A:
   - Here, and are hypotenuses, and and are legs.
Since (hypotenuses are congruent) and

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