Answer :

Final answer:

The methods used to prove that triangles are congruent include Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Side-Side-Side (SSS). Side-Side-Angle (SSA) is not a reliable method for proving triangle congruence due to its ambiguity.

Explanation:

In triangle congruence, three methods are commonly used. These include the Side-Angle-Side (SAS) method, the Angle-Side-Angle (ASA), and the Side-Side-Side (SSS) method.

In the SAS method, if two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle then the triangles are congruent.

According to the ASA method, if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle then the triangles are congruent.

Finally, the SSS postulate states that if the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

However, the Side-Side-Angle (SSA) condition does not apply in most cases. This condition, known as the 'ambiguous case', could result in one, two, or no triangles at all.

Learn more about Triangle Congruence here:

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