# GeoGebra

## Special Centers of Triangles

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.

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.

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

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.

Perpendicular 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.

Incenter Investigation, created by Natalie Klein

Centroid Construction, created by Natalie Klein

Centroid Investigation, created by Natalie Klein

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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