There are five criteria in geometry for studying the congruence of any two triangles. Here is the list of possible criterion for determining the congruent triangles.
The triangles are congruent if the lengths of sides of a triangle are equal to the lengths of corresponding sides of other triangle.
The triangles are congruent if the lengths of two sides and the included angle of a triangle are equal to the lengths of two corresponding sides and the included angle of other triangle respectively.
The triangles are congruent if two angles and the length of included side of a triangle are equal to the corresponding two angles and the length of included side of other triangle respectively.
The triangles are congruent if two angles and the length of a side of a triangle are equal to the corresponding two angles and the length of side of other triangle respectively.
The right triangles are congruent if lengths of hypotenuse and one side of a triangle are equal to the lengths of hypotenuse and corresponding one side of other triangle respectively.
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