Option B pair of triangles cannot be proved congruent.
Congruence in two or more triangles depends on the measurements of their sides and angles. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. They are of the same shape and size.
SSS Criterion for Congruence
SSS criterion stands for Side-Side-Side criterion. Under this criterion, two triangles are congruent if three sides of a triangle are equal to the corresponding sides of the other triangle.
SAS Criterion for Congruence
SAS criterion stands for Side-Angle-Side criterion. Under this criterion, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.
ASA Criterion for Congruence
ASA criterion stands for Angle-Side-Angle criterion. Under the ASA criterion, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.
AAS Criterion for Congruence
AAS criterion stands for Angle-Angle-Side criterion. Under the AAS criterion, two triangles are congruent if any two angles and the non-included side of one triangle are equal to the corresponding angles and the non-included side of the other triangle.
According to the question
Option A :
SAS : A triangle with equal sides and equal angles.
Option C :
SSS : A triangle with equal sides.
Option D :
AAS : A triangle with two equal angles and one equal side.
Option B :
These pair of triangles cannot be proved congruent.
Two triangles with equal corresponding angles may not be congruent to each other because one triangle might be an enlarged copy of the other. Hence, there is no AAA criterion for congruence.
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