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 GF is parallel to segment EB.

Segment EG is parallel to segment BH.

Segment BH is congruent to segment HC.

Segment EG is congruent to segment GD.

Answer 1

please help
@Callisto @Hero @jim_thompson5190

Answer 2

@jim_thompson5910

Answer 3

The segment of a triangle that joins the midpoints of two sides of a triangle is parallel to the third side of the triangle.

http://www.regentsprep.org/Regents/math/geometry/GP10/MidLineL.htm

Answer 4

Applying the theorem to the marked up diagram:

Segment EG is parallel to segment BH.

@sIllyg00se