c. Theorem 3. The altitudes of a triangle meet in a point. In Figure 3-24, point P is where the

altitudes meet.

d. Theorem 4. The angle bisectors of a triangle meet in a point that is equidistant from the three

sides. Figure 3-25 shows that the angle bisectors of a triangle meet at point P. Perpendicular lines from

the sides (XP, YP, and ZP) are of equal length.

e. Theorem 5. The medians of a triangle meet at a point that is two-thirds of the distance from

each vertex to the midpoint of the opposite side, see Figure 3-26. A median is a line from the vertex to

the midpoint of the opposite side of a triangle. Point P is called the centroid of the triangle because this

point is the center of gravity.