**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
the triangle.
**

Caution: The orthocenter is NOT the center
of any one of the circles of the triangle.

5 - PERPENDICULAR BISECTORS OF A TRIANGLE