Geometry · Rectangle · Midpoints · Isosceles triangle · Congruent triangles · Angle chase
Let \(E\) and \(F\) be the midpoints of the sides \(AD\) and \(DC\) of a rectangle \(ABCD\), and let \(G\) be the point where the segments \(AF\) and \(EC\) cross. Prove that
\[ \angle CGF = \angle FBE . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2004, 1. letnik, category A, problem 3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source