I have a vertical line EF and two lines which are nearly horizontal but obviously not parallel on the left of EF. I need to find points X and Y, one on each of the two unnamed lines shown, such that XY=EF and XY is parallel to EF.

I can find a line parallel to another line if I have a point it's supposed to pass through and I can make a segment which is congruent to another segment but this seems to require more. If it's any help, it's in a chapter that has to do with reflections and translations.