This is a visual glossary of various objects associated with any triangle in Euclidean geometry. [br][br](The notation used here is meant to match Section 5.6 of Venema's [url=http://www.calvin.edu/~venema/geometrybook.html][i]Foundations of Geometry[/i][/url].)

The vertices [color=#ff0000]A[/color], [color=#ff0000]B[/color], and [color=#ff0000]C[/color] may be moved around at will.[br][br]There are many beautiful facts to be discovered, at all levels of difficulty (from fairly simple to very deep), about the objects illustrated here. For example, here are just a few things to notice:[br][list][br][*] The [color=#009900]centroid[/color] has a famous physical significance -- it's sometimes known as the "center of balance." How can we be sure of this property?[br][*] Why can we be sure that the three [color=#ff9900]perpendicular bisectors[/color] will always meet in a single point?[br][*] Display the [color=#009900]centroid[/color], [color=#0000ff]orthocenter[/color], and [color=#ff9900]circumcenter[/color] at the same time. What do you notice about them? And what about the [color=#ff33cc]incenter[/color]?[br][/list]