question_answer

In two triangles ABC and PQR, BC = QR, AB = PQ and extended m \[\angle ABC=120{}^\circ \] and extended m \[\angle PQS=120{}^\circ .\]Then, by which condition are the two triangles congruent?                                             [SSC (CGL) Pre 2014]

A) Side - Angle - Side  

B) Angle - Side - Side

C) Angle - Side - Angle

D) Side - Side - Side

Correct Answer: A

Solution :

 

In figure, \[\Delta ABC\] and \[\Delta PQR\] are similar triangle.

Here, \[\overline{BC}=\overline{QR},\,\]\[\overline{AB}=\overline{PQ}\]

and \[\angle B=\angle Q=120{}^\circ \]

Hence, both triangles are congruent by the condition of side-angle-side.