Question

1. choose the correct answer.

which triangle illustrates a centroid?
d
b
a
c

Explanation:

The centroid of a triangle is the point of intersection of its medians. A median of a triangle is a line segment joining a vertex to the mid - point of the opposite side. In option A, the segments \(AX\), \(BY\), and \(CZ\) are medians (since \(Y\) is the mid - point of \(AB\), \(Z\) is the mid - point of \(BC\), and \(X\) is the mid - point of \(AC\)) and \(P\) is the centroid. The property of the centroid is that the centroid divides each median in a ratio of \(2:1\). For example, \(AP=\frac{2}{3}AX\), \(BP = \frac{2}{3}BY\), \(CP=\frac{2}{3}CZ\).

Option B shows the in - center (intersection of angle bisectors). Option C shows the ortho - center (intersection of altitudes). Option D shows the circum - center (intersection of perpendicular bisectors).

Answer:

A.