By applying which of the following criteria can two triangles NOT be proved congruent?

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To prove two triangles congruent, we use certain criteria: SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), and AAS (angle-angle-side). The 'angle-angle-angle' (AAA) criterion only ensures similarity, not congruence, because triangles with the same angles can have different side lengths (they are similar but not necessarily congruent). Therefore, triangles cannot be proved congruent by the AAA criterion.

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