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 GD is congruent to segment GF.
Segment GD is parallel to segment HC.
Segment GF is parallel to segment EB.
Segment BH is congruent to segment HC.

Answer 1

@mathstudent55

Answer 2

@jhonyy9

Answer 3

Can somebody please help?

Answer 4

Look at this part of the drawing.

Answer 5

Remember that BD is a median, so segments AD and CD are congruent.
Ok?

Answer 6

Also, remember how point H was place where it is.
It was placed in a way that segment GH is congruent to segment AG.
Now we have this:

Answer 7

Do you follow so far?

Answer 8

yeah

Answer 9

Are you familiar with the side splitter theorem?

Answer 10

uhhh, no

Answer 11

Side splitter theorem
If a line is parallel to a side of a triangle and intersects the other two sides, then it divides the other sides into proportional segments.

Answer 12

You have a triangle, call is triangle ABC.

Answer 13

Now draw a line parallel to side BC that intersects the other two sides of the triangle at points D and E.

Answer 14

By the side splitter theorem, then segments AD and BD are proportional in length to segments AE and EC.

Answer 15

The converse of that theorem is also true.
If a line intersects two sides of a triangle, such that the segments of the intersected sides are proportional, then the line is parallel to the third side.

Answer 16

ok

Answer 17

Now look at your simplified case above.
You don't need to go above looking for it.
Here it is again below.