Geometry Problem 763: Parallelogram, Diagonal, Parallel, Congruence.

The figure shows a parallelogram ABCD with EF parallel to the diagonal AC. DE and DF meet AC at G and H, respectively. Prove that AG and CH are congruent.
 

See also:
Isolines of problem 763.

Dynamic Geometry: GeoGebra applet

Created with GeoGebra by Tim Brzezinski

Problem 763 on Twitter

1 Parallelogram + 1 Diagonal + 1 Parallel Ray = 😮? How can we formally prove the congruence illustrated here? Source: @gogeometry. https://t.co/bUi4oNHKGU @geogebra #MTBoS #ITeachMath #math #maths #EdTech #geometry #proof #MathEd #HSMath #CollegeMath pic.twitter.com/ckhcyyAhsz

— Tim Brzezinski (@Brzezinski_Math) January 11, 2020