Question

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

Answer:

Correct option is B

Step-by-step explanation:

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

we have to find the conclusion from above information.

In ΔAHC

AG=GH     (∵ Given)       →    (1)

As BD is the median of ΔABC bisecting AC at D,

∴ AD=DC                        →    (2)

From equation (1) and (2), we get

G and D are the mid-point of sides AH and AC respectively.

Hence, by mid-point theorem, which states that the line joining the midpoints of two sides of a triangle is parallel to the third side and is equal to one half of the length of third side.

Hence, GD||HC i.e GD is parallel to HC

∴ option B is correct.

Answer 2

I believe the correct answer would be Segment GD is parallel to segment HC.  Hope this helped!

-TTL