Mr. Perkins wants to compare the number of golf players on his course on a weekday versus a weekend. He records the number of golfers every hour on a randomly chosen weekday, and again on a randomly chosen weekend.

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.