To prove triangles congruent, the appropriate theorem to use depends on the information given about the triangles. Here's a brief overview of each theorem:
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SSA Congruence Theorem: This theorem states that if two sides and a non-included angle are known, it does not guarantee triangle congruence. Thus, it is not a valid method for proving congruence.
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ASA Congruence Theorem: This theorem states that if two angles and the included side are known, then the two triangles are congruent.
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SSS Congruence Theorem: This theorem states that if all three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.
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SAS Congruence Theorem: This theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
If you need to prove two triangles are congruent and you have the measures of two sides and the angle in between (SAS), you would use the SAS Congruence Theorem. If it's two angles and the side between them (ASA), then use the ASA Congruence Theorem. If you have three sides (SSS), then use the SSS Congruence Theorem.
In conclusion, what information do you have about the triangles? That will guide which theorem you should use to prove their congruence.
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