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?

A.)Segment GF is congruent to segment EG.
B.)Segment GF is half the length of segment EB.
C.)Segment GD is congruent to segment EG.
D.)Segment GD is half the length of segment HC.

Answer 1

please help

Answer 2

fill in some ddata on then triangle

Answer 3

what?

Answer 4

well like label the medians

Answer 5

i wanna say the answer is C but im still not sure

Answer 6

Ok, I got it.

Answer 7

Look at triangle ACH.

Answer 8

D is the midpoint of side AC.
point H was placed purposely to make segments GH and HG congruent.
That means that point G is the midpoint of segment AH.
AH is a side of triangle ACH.
GD is a segment that connects the midpoints of two sides of a triangle.
There is a theorem that deals with this situation.
Do you know it?