Question

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Answer 1

Answer: GE -0 CD-12 BG-36

Explanation:

The length of GE is zero because point G is the centroid of

triangle ABC, which means that the medians AE, BF, and CD intersect at

G. The centroid divides each median into segments in a 2:1 ratio. So, if GE

represents the length of the segment from G to E, and CE represents the

length of the entire median CD, then GE is 1/3 of CE. Therefore, if CE is

known to be 0, GE will also be 0.

To find the length of CD, we need to use the fact that the centroid

divides each median into segments in a 2:1 ratio. Given that GD is 4, we

can find the length of the entire median CD by multiplying GD by 3. So, CD

= 4 * 3 = 12.

Similarly, to find the length of BG, we multiply the known length of

BF (12) by 3. Therefore, BG = 12 * 3 = 36.

Answer 2

Applying the centroid theorem, the values of the measures are: GE = 5; CD = 12; BG = 8.

What is the centroid theorem?

The theorem about the centroid asserts that the point where the medians of a triangle intersect is located at two-thirds of the distance from each vertex to the midpoint of the corresponding side. In this case, it means:

BG = 2/3(BF)

AG = 2/3(AE)

CG = 2/3(CD)

Find GE:

AG = 2/3(AE)

10 = 2/3(AE)

30 = 2*AE

AE = 15

GE = AE - AG

GE = 15 - 10

GE = 5

Find CD:

GD = 1/3(CD)

4 = 1/3(CD)

12 = CD

CD = 12

Find BG:

BG = 2/3(BF)

BG = 2/3(12)

BG = 8