Final answer:
Angles LMQ and LNQ are congruent because line LQ bisects angle MN, and the segments LM and LN are equal, which by the Side-Angle-Side postulate, ensures the triangles LMQ and LNQ are congruent and thus their corresponding angles are equal.
Step-by-step explanation:
The student's question relates to determining why angles LMQ and LNQ are congruent given that line LQ is the bisector of MN and the segments LM and LN are equal.
To demonstrate that these angles are congruent, we can refer to the fact that the bisector of an angle divides the angle into two equal parts.
Therefore, if LQ is the bisector of angle MN, then it would divide it into two equal angles, LMQ and LNQ.
Since LM is equal to LN, it also implies that the triangles formed, LMQ and LNQ, are congruent by the Side-Angle-Side (SAS) postulate.
Thus, the angles LMQ and LNQ are also congruent.