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To prove triangles are congruent by the Hypotenuse-Leg (HL) theorem, you need to establish that both triangles have a right angle, and that the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle, respectively. An additional congruence statement that could be used is that the lengths of the hypotenuses of both triangles are equal, along with confirming that one leg in each triangle is also equal in length. This information is sufficient to apply the HL theorem for congruence.

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