Question

given that point b is the centroid of △cde, which of the following is true? segment eg bisects angle dej. the length of jb is half of the length of db. the length of hb is half of the length of hc. two of these are true. additional information ge = 12.3

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a ratio of 2:1. A median is a line - segment joining a vertex to the mid - point of the opposite side.

Step2: Analyze each option

• Option A: There is no information to suggest that segment EG bisects angle DEJ. A centroid has no property related to angle - bisection.
• Option B: JB and DB are not part of a median - centroid relationship. The centroid divides the median from a vertex to the mid - point of the opposite side.
• Option C: Since B is the centroid and HC is a median (assuming H is the mid - point of DE), by the centroid property, the centroid B divides the median HC such that HB:BC = 1:2, or HB is half of HC.

Answer:

C. The length of HB is half of the length of HC.