A Median Surprise

Let $D,E,F$ be the midpoints of the sides of ΔABC, as shown below. Rotate triangles $CDG,AEG,BFG$ $180∘$ around points $D,E,F$, respectively, into triangles $BDG_b,CEG_c,AFG_a$.

This procedure creates three congruent triangles: $AGG_a, BGG_b$, and $CGG_c$.

Read more »