Final answer:
None of the statements A to D are necessarily true if triangle AJKL is congruent to triangle AMNP; each side or angle should be congruent to its corresponding counterpart, and none of the given options correctly identify those counterparts.
Step-by-step explanation:
If triangle AJKL is congruent to triangle AMNP, then corresponding parts of congruent triangles are equal. This means that corresponding sides and angles of the two triangles must be congruent. In this case, side JK would be congruent to side MN, side KL would be congruent to side NP, and side LJ would be congruent to side PM. Additionally, angle J would be congruent to angle M, angle K to angle N, and angle L to angle P.
To answer your question directly, from the options given:
A) JK is congruent to MP is incorrect because JK should be congruent to MN.
B) Angle K is congruent to angle M is incorrect because Angle K should be congruent to angle N.
C) KL is congruent to MP is incorrect because KL should be congruent to NP.
D) JK is congruent to KL is not necessarily true as there is no information suggesting that triangle AJKL is an isosceles or equilateral triangle where two sides can be congruent.
None of the options provided are correct based on the information given about the congruent triangles.