Lab 8 Investigating Triangle Centers __

Lab 8 … Investigating Triangle Centers __

The 9 point center

Objectives:

1. Create a GSP drawing of one of the CLASSICAL TRIANGLE CENTERS

2. Create a 1 page word document, Print Screen and paste in your GSP drawing.

3. Include a description of the center you chose with any biographical or historical anecdotes that you can discover. Make the page visually appealing and informative for full credit. Treat the page as your introduction of this remarkable center to a group of people who know basic geometry.

Requirements:

1. Email your word document: [email protected] due by 5/30 TRIANGLE CENTERS Long before the first pencil and paper, some curious person drew a triangle in the sand and bisected the three angles. He noted that the bisectors met in a single point and decided to repeat the experiment on an extremely obtuse triangle. Again, the bisectors concurred. Astonished, the person drew yet a third triangle, and the same thing happened yet again!

Unlike squares and circles, triangles have many centers. The ancient Greeks found four: incenter, centroid, circumcenter, and orthocenter. A fifth center, found much later, is the Fermat point. Thereafter, points now called nine- point center, symmedian point, Gergonne point, and Feuerbach point, to name a few, were added to the literature. In the 1980s, it was noticed that these special points share some general properties that now form the basis for a formal definition of triangle center

The Encyclopedia of Triangle Centers lists many centers, but without pictures. The purpose of this page is to introduce a collection of individual pictures, showing constructions of selected triangle centers. The selections are in two groups: Recent Triangle Centers and Classical Triangle Centers Recent Triangle Centers Centroid Schiffler Point Incenter Exeter Point Circumcenter Parry Point Orthocenter Congruent Isoscelizers Point Fermat Point Yff Center of Congruence Nine-point center Isoperimetric Point and Equal Detour Point Symmedian point Ajima-Malfatti Points Gergonne point Apollonius Point Nagel point Morley Centers Mittenpunkt Hofstadter Points Spieker center Equal Parallelians Point Feuerbach point Bailey Point Isodynamic points Gossard Perspector Napoleon points Steiner point Classical Triangle Centers

In addition to triangle centers, there are many interesting central lines, too. The most famous is the Euler line.

The Encyclopedia of Triangle Centers Web Address: http://faculty.evansville.edu/ck6/tcenters/index.html