Question

1. choose the correct answer.

which triangle involves medians?
a
d
c
b

Explanation:

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. The centroid \(P\) of a triangle divides each median in a ratio of \(2:1\). Here \(AP=\frac{2}{3}AX\), \(BP = \frac{2}{3}BY\), \(CP=\frac{2}{3}CZ\) which is a property of the centroid (the point of intersection of medians).
Option B involves angle - bisectors (as the angles at \(A\) and \(B\) are bisected). Option C involves altitudes (since there are right - angle markings at the feet of the segments from \(A\), \(B\), and \(C\) to the opposite sides). Option D involves perpendicular bisectors (as the segments from \(A\), \(B\), and \(C\) are perpendicular to the opposite sides and bisect them).

Answer:

A.