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