GeoGebra

Special Centers of Triangles

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Htm.gif Special Centers of Triangles Zip.gifDownload Created by Cullen G.E. Stevens

Special centers of triangles can be found by finding the point of concurrency of different lines. The circumcenter of the triangles is the point of concurrency of the perpendicular bisectors of the triangle. Similarly, the point of concurrency of the angle bisectors is called the incenter of the triangle, the medians produce the centroid, and the altitudes the orthocenter.

The included example displays four congruent triangles and one of the special centers. Change the upper left triangle (all triangles will remain congruent) to examine how the special centers are affected.

Zip.gif Triangle Tools Download Created by David Corne This is a useful tool for finding many of the special centres of triangles including the orthocentre, centre of gravity, incentre and circumcentre. It will also construct medians, inscribed and circumscribed circles.

Htm.gif Segments and Circles of a Triangle, created by Dimitris Poimenidis

Htm.gif Circles and Centers of Triangles, created by Anders Sanne. This inquiry based teaching materials consist of several dynamic worksheets linked together.

Htm.gif Perpendicular Bisectors Part I, created by Megan Mulert. This dynamic worksheet is the first of two intended to act as an introduction to the circumcenter of a triangle. This dynamic worksheet helps to show that any point on a perpendicular bisector is equidistant from the endpoints of the segment it bisects.

Htm.gifPerpendicular Bisectors Part II, created by Megan Mulert. This dynamic worksheet is the second of two intended to act as an introduction to the circumcenter of a triangle.

Perpendicular Bisectors Worksheet created by Megan Mulert. This worksheet includes questions to focus thinking while working in the two dynamic worksheets included above.

Htm.gif Incenter Investigation, created by Natalie Klein

Htm.gif Centroid Construction, created by Natalie Klein

Htm.gif Centroid Investigation, created by Natalie Klein

Htm.gif Comparing Circumcenter, Incenter, and Centroid, created by Natalie Klein

Htm.gif Triangle Concurrency Points, created by Stephen Kent Stephenson.
Shows all concurrency points of any triangle, along with its Euler Line and 9-point circle.

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