Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?

Segments OM and LP intersect at point N; triangles are formed by points LNM and ONP; line k intersects with both triangles at point N.

Use rigid and nonrigid transformations to prove segment PN over segment MN = segment LN over segment ON.
Use a rigid transformation to prove that ∠NPO ≅ ∠NLM.
Use rigid and nonrigid transformations to prove segment PN over segment ML = segment LN over segment ON.
Use a rigid transformation to prove that ∠NLM ≅ ∠LMN.