# Math Help - A hard construction

1. ## A hard construction

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.

2. Hi

Consider the translation $\overrightarrow{EF}$
X is transformed into Y
X being on the upper line, its image by the translation is on the image of the upper line
Since it is Y, it is also on the lower line
Therefore it is at the intersect of the lower line and the image of the upper line
Draw the image of the upper line and find the intersect with the lower line