Answer: The correct option is d, i.e., Segment EG is half the length of segment BH.
Explanation:
It is given that the triangle ABC with medians FA, BD, and CE. Segment FA is extended to H in such a way that segment GH is congruent to segment AG.
Since FA, BD, and CE are median it means the points D,E,F are the midoint of the line AC, AB, BC respectively.
It is also given that the line segment GH is congruent to segment AG. It means the point G is the mid point of the line segment AH.
In trianle ABH the line EG is joining the midpoint of AD and AH. So by using midpoint theorem of triangle we can say that the line EG and BH are parallel lines and the length of EG is half of the length of BH.
Therefre option d is correct.
