Answer :

Final answer:

The methods that could be used to prove the triangles congruent are SSS (Side-Side-Side), SAS (Side-Angle-Side), and ASA (Angle-Side-Angle). The SSA (Side-Side-Angle) method isn't valid for proving triangle congruence.

Explanation:

In order to prove that triangles are congruent, we can use any of the three methods: Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA). SSS states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. SAS states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Furthermore, ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. The SSA method is not a valid method for proving triangles congruent because it does not necessarily produce a unique triangle.

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