Bold = reason (in reasons 3 and 4 the formatting is odd and goes into the next line)
Statement Reason
1. line segment ʜᴏ is parallel to line segment EL, 1. Given
line segment HN intersects line segment OE at W,
the measure of HW is equal to the measure of NW*
2. angle HWO is congruent to angle NWE 2. Vertical angle theorem
3. angle OHW is congruent to angle WNE 3. alternate interior angles theorem
*4. line segment HW is congruent to line segment NW 4. definition of congruent
5. triangle HOW is congruent to triangle NEW 5. ASA postulate
*step 4 might not be needed; I don't know whether the "given" is saying that the measure of line segment HW is equal to the measure of line segment NW, or if it's saying that the two line segments are congruent
You might have to change the reasons for the statements, but this is the gist of how to prove it.