Geometry

Question Analysis:
This question is about identifying valid justifications for proving the congruence of two right triangles.
The main focus is on understanding the different triangle congruence criteria and how they apply specifically to right triangles.

Key Concept Explanation:
HL (Hypotenuse - Leg): If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, the two right triangles are congruent.
SSS (Side - Side - Side): When all three sides of one triangle are congruent to the corresponding three sides of another triangle, the triangles are congruent.
This applies to all triangles, including right triangles.
SAS (Side - Angle - Side): Two sides and the included angle of one triangle must be congruent to the corresponding two sides and included angle of another triangle.
In right triangles, this can be used when the right angle is the included angle between two known sides.
AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, the triangles are congruent.
This also applies to right triangles.

Step - by - Step Solution:
Analyze option A:
Having two congruent legs and one congruent angle it satisfies the SAS (Side - Angle - Side) congruence criterion.
The right angle is between the legs. So, this option is correct.
Analyze option B:
This is the HL (Hypotenuse - Leg) criterion. If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent. So, this option is correct.
Analyze option C:
When the triangles have three congruent sides, it satisfies the SSS (Side -...