EMAT 6690


~Circumcenter~Orthocenter~ 

~Euler Line ~


A perpendicular bisector is a line that bisects and is perpendicular to the side of a triangle.  The point of concurrency of the perpendicular bisectors is called the circumcenter of a triangle.

An investigation than can be used as a teaching tool for the circumcenter.

Investigation


An altitude is a perpendicular line drawn from a vertex of a triangle to the opposite side.  The point of concurrency of the altitudes is called the orthocenter of a triangle.

An investigation than can be used as a teaching tool for the circumcenter.

Investigation


The Euler Line is always contains three of the four points of concurrency.  THe Euler Line is named after Swiss mathematician Leonhard Euler, who proved that the three points of concurrency were collinear.

An investigation that can be used as a teaching tool for the Euler Line.

Investigation

Students should be able to complete the following conjecture at this point.

The -(centroid)-,-(circumcenter)-, and the -(orthocenter)- are the three points of concurrency that always lie on the Euler line.

Students should be able to complete the following conjecture at this point.

The -(centroid)- divides the Euler segment into two parts so that the smaller part is -(half as long as)- the larger part.


Student Activity


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