Figure 3-23. Perpendicular bisectors
c. Theorem 3. The altitudes of a triangle meet in a point. In Figure 3-24, point P is where the
Figure 3-24. Altitudes
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.
Figure 3-25. Angle bisectors
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.