Leah wants to prove the Alternate Interior Angles Theorem. In the diagram,
CE
H
DF | GI.
Complete Leah's proof that alternate interior angles ZDEH and ZIHE are congruent.
Construct the midpoint M of EH then rotate DF, GI, and EH 180° about M to get D'F', GT,
and E'H'. Since M lies on EH and the rotation is 180°, E'H' coincides with
. E and H
are equidistant from M on EH, so E' coincides with
and E'H' coincides with
A 180° rotation of a line is a parallel line, and the only line parallel to DF that passes through
His ▼. Therefore, D'F' and GI coincide and E'D' and
maps ZDEH onto ZIHE. Since rotation
coincide. So, the rotation
ZDEH ZIHE.