Question

Consider the figure below.

Line segment AD, Line segment BE, and line segment CF are medians concurrent at G.
Which of the following statements is true?

A FG=1/2 GC
B ED=2/3 AB
C BG=1/2 BE
D GD=2/3 AD

Answer 1

A: FG = ½GC

Explanation:

Since AD, BC and CD are medians concurrent at G, it means G is the centroid.

Now, when median passes through the centroid, the centroid divides the median in the ratio of 2:1.

Also,that the median touches the side of the triangle at their midpoints.

Thus,by inspection, we can say that;

GD = ⅓AD

GC/FG = 2/1

Thus, GC = 2FG and FG = ½GC

BG = ⅔BE

Tbus,looking at the options given and what we have gotten in proof, we can say only FG = ½GC is correct.