Question

$△$ ABC and $△$ DEF are two triangles, then to ensure that two triangles ABC and DEF are congruent, 3 conditions given; AB = DE, AC =DF, $\angle$ ABC = $\angle$ DEF are

• A. sufficient but not necessary
• B. necessary but not sufficient
• C. neither necessary nor sufficient
• D. both necessary and sufficient

Answer 1

The correct option is B necessary but not sufficient

Given that two sides of the triangle are same and one of the angles (non-included angle) are same.
If the two triangles are congruent, then it is necessary for the third side to also be same or the included angle to be same.
However, this information is not provided.
Hence the information provided is necessary but not sufficient to prove congruence.