Sinje Butler

**Write-up 4**

The **CENTROID (G)** of a triangle is the common
intersection of the three medians.

As the shape of the triangle changes the centroid always
remains inside. Please see** GSP
demonstration **and move one point of triangle to notice the
changes taking place**. **

The **ORTHOCENTER (H) **of
a triangle is the common intersection of the three lines containing the
altitudes.

It should be clear that as the shape of the triangle
changes, **H** does not always fall inside
the triangle. Please see** GSP demonstration **and
move one point of triangle to notice the changes taking place.

The **CIRCUMCENTER (C) **of
a triangle is the point in the plane equidistant from the three vertices of the
triangle. **C** is on the perpendicular bisector of each side of
the triangle. Notice that as the triangle changes shape the circumcenter does
not always stay inside. Please see** GSP demonstration** and move one point of
triangle to notice the changes taking place**.**

Note that the circumcenter is the center of the **CIRCUMCIRCLE**. The
circumcircle is constructed by drawing a segment from the circumcenter to one
of the vertices and using this segment as the radius of the circle.

** **

Please see** GSP demonstration **and move one point of
triangle to notice the changes in the length of the of the radius** **.

The **INCENTER (I)** of
a triangle is the point on the interior of the triangle that is equidistant
from the three sides. **I **is on the angle bisector of each angle of the
triangle.

Please see** GSP
demonstration **and move one point of the triangle to notice the
changes.

The incenter is the center of the **INCIRCLE** (the inscribed circle) of the triangle. The incenter is constructed by drawing
a segment from the incenter perpendicular to one of the sides of the triangle
and using this segment as the radius of the circle.

Please see** GSP
demonstration **and move one point of the triangle to notice the
changes.

The following is a construction of **G, H, C, **and **I **for
the same triangle.

Please see** GSP
demonstration **and move one point of the triangle to notice the
changes.