Question

The figure shows triangle ABC with medians AF, BD, and CE. Segment AF is extended to H in such a way that segment GH is congruent to segment AG.

Triangle ABC with medians CE, AF, and BD. Median AF is extended to point H. A segment joins points B and H and another segment joins points H and C.

Which conclusion can be made based on the given conditions?

Segment EG is congruent to segment GD.
Segment GF is half the length of segment EB.
Segment BG is congruent to segment GC.
Segment EG is half the length of segment BH.