The **Centroid** is the central point of the triangle which the 3 medians cross over. The centroid lies two-thirds of the distance from each vertex to the midpoint on its opposite side. The medians and centroid can be visually represented as such:

Using the points given by the centroid, the length of the median can be determined using the following formula(s), referred to as the **Segment Addition Postulate**:

\(\text{XM} = \cfrac{2}{3}\text{XM} + \cfrac{1}{3}\text{XM}\)

Determine the respective lengths of \(\text{PC}\) and \(\text{MC}\) if the length of \(\text{PM}\) is \(30\).

We can use Segment Addition Postulate to determine the missing side lengths:

\(\text{PC} = \cfrac{2}{3}(30) = 20\)

\(\text{PC} = 20\)

\(\text{MC} = \text{PM} - \text{PC}\)

\(\text{MC} = 30 - 20 = 10\)

\(\text{MC} = 10\)

Therefore, we can determine that \(\text{PC}\) and \(\text{MC}\) have respective side lengths of \(20\) and \(10\).

Determine the respective lengths of \(\text{TM}\) and \(\text{MC}\) if the length of \(\text{TC}\) is \(8\)

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