AUXILIARY ELEMENTS OF A TRIANGLE
1 - MEDIANS OF A TRIANGLE
If the above triangle has an infinitesimal thickness and mass, then we can think of the centroid as its center of gravity: All of its weight can be considered as being concentrated at the centroid.
Caution: The centroid is NOT the center of any one of the circles of the triangle.
2 - INTERIOR ANGLE BISECTORS OF A TRIANGLE
In Figure 4.3 above, AD is the angle bisector that divides angle BAC into two congruent parts.
3 - EXTERIOR ANGLE BISECTORS OF A TRIANGLE
The bisectors of a triangle's exterior angles are concurrent. Their common point is the excenter of the triangle. A triangle has three excenters.
4 - ALTITUDES OF A TRIANGLE
Altitudes of a triangle are concurrent. The
intersection point is the orthocenter of
Caution: The orthocenter is NOT the center of any one of the circles of the triangle.
5 - PERPENDICULAR BISECTORS OF A TRIANGLE