Question

If J is the centroid of triangle CED, DE = 52, FC = 15, and HE = 14, find each measure.

Answer 1

Using the property of the centroid, we can find the measures of the segments in triangle CED. JD = 104/3, CJ = 10, and EJ = 28/3.

Step-by-step explanation:

To find the measures of the segments in triangle CED, we can use the property of the centroid, which states that the centroid divides each median into two segments, with the distance from the centroid to the vertex twice as long as the distance from the centroid to the midpoint of the opposite side.

Since J is the centroid of triangle CED, we can find the lengths of JD, CJ, and EJ by applying this property:

1. DE = 52, so JD = 2 * DJ = 2 * (52/3) = 104/3
2. FC = 15, so CJ = 2 * FJ = 2 * (15/3) = 10
3. HE = 14, so EJ = 2 * HJ = 2 * (14/3) = 28/3

Therefore, the measure of JD is 104/3, the measure of CJ is 10, and the measure of EJ is 28/3.