Examine the paragraph proof. which theorem does it offer proof for?

segments jk and hi are parallel, segment lo intersects segment jk at point n, segment lo intersects segment hi at point m, and points n and m are between points l and o on segment lo.

prove: ∠jnm ≅ ∠nmi

according to the given information in the image, segment jk is parallel to segment hi while ∠jnm and ∠lnk are vertical angles. ∠jnm and ∠lnk are congruent by the vertical angles theorem. because ∠lnk and ∠nmi are corresponding angles, they are congruent according to the corresponding angles theorem. finally, ∠jnm is congruent to ∠nmi by the transitive property of equality.

answers:

alternate interior angles theorem

corresponding angles theorem

vertical angles theorem

same-side interior angles theorem