Explanation:
There are probably several different strategies that could be used to show NK≅LM. One that comes to mind is to show AAS congruence of triangles NKL and LMN, then claim the sides are congruent by CPCTC (corresponding parts of congruent triangles are congruent). So, the first three boxes on the left will be filled with congruence statements for the angles and side.
- ∠K ≅ ∠M . . . . given
- ∠KLN ≅ ∠MNL . . . . alternate interior angles where a transversal (LN) crosses parallel lines (KL, MN)
- LN ≅ NL . . . . reflexive property
Now, we have two corresponding angles and a corresponding side of triangles NKL and LMN, so we can claim
- ΔNKL ≅ ΔLMN . . . . AAS congruence theorem
And that lets us draw the desired conclusion
