The student needs to prove the congruency of triangles AJKL and ANKM by using given information. The key steps involve using the fact that K is the midpoint of two segments and employing the Side-Side-Side (SSS) Postulate for congruence.
Step-by-step explanation:
The student is tasked with proving that two triangles, AJKL and ANKM, are congruent given a set of preconditions. The fact that JL = NM and K is the midpoint of both JN and LM leads to further steps in the proof:
Given: JL = NM.
K is the midpoint of JN and LM (Given).
From step 2, we can infer that JK = NK and LK = MK because the definition of a midpoint is such that it divides a segment into two equal parts.
With JK = NK and LK = MK, along with the matching sides JL = NM given initially, by the Side-Side-Side (SSS) Postulate, the triangles AJKL and ANKM are congruent.