1) Congruence in Geometry:
o Two triangles are said to be congruent when all their corresponding sides and angles are equal.
o The criteria for congruence are SSS, SAS, ASA, AAS, and RHS (for right-angled triangles).
2) Analysis of Options:
o Option 1: As a triangle is said to be congruent if any two or all conditions of all the three sides being same, their perimeter being the same or their areas being the same are fulfilled. So, it is congruent.
o Option 2: Same area and base do not guarantee congruence, as the shape can differ (e.g., one triangle may be obtuse, the other acute).
o Option 3: One side and one angle are not sufficient, as the remaining dimensions can vary.
o Option 4: If two triangles have the same base and height, they may or may not be congruent
The correct answer is Option 1.
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