Questions: Given that point B is the centroid of triangle CDE, which of the following is true? The length of BG is half of the length of EB. The length of BG is one-third of the length of EG.

Given that point B is the centroid of triangle CDE, which of the following is true?
The length of BG is half of the length of EB.
The length of BG is one-third of the length of EG.

Transcript text: Given that point B is the centroid of $\triangle C D E$, which of the following is true? The length of $B G$ is half of the length of EB. The length of BG is one-third of the length of EG.

Solution

Solution Steps

Step 1: Understand the properties of a centroid

The centroid of a triangle is the point where the three medians of the triangle intersect. A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. The centroid divides each median in a 2:1 ratio.

Step 2: Apply the centroid properties to the given information

Since B is the centroid of triangle CDE, and EG is a segment connecting vertex E and a point G on the opposite side CD, BG is part of the median EB. Since B is the centroid, it divides the median in a 2:1 ratio. This means that BG is 1/3 of the length of EG and also that BG is 1/2 the length of BE.

Final Answer

The length of BG is one-third of the length of EG.

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