EMAT 6690


~ Centroid  ~ Incenter  ~


For the next two days we will explore points of concurrency.  The point of concurrency is the point where concurrent lines intersect.  This is a single point.

Materials needed for this lesson are wax paper, straightedge, and pencil.

Students will need to have access to Geometer's Sketchpad.


A triangle has many special lines: medians, angle bisectors, perpendicular bisectors, and altitudes to name a few.  Each triangle has three of the previously mentioned lines.


A median is a line drawn from a vertex to the midpoint of the opposite side.   The point of concurrency of the medians is called the centroid of the triangle.

Investigations that can be used as teaching tools for the centroid.

Investigation #1

 Investigation #2

    

 

Students should be able to complete the follow conjecture after completing the student activity with Geometer's Sketchpad.

The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is -(twice)- the distance from the centroid to the midpoint.


An angle bisector is a ray that divides an angle into two congruent angles.  The point of concurrency of the angle bisectors is called the incenter of the triangle.

Investigations that can be used as teaching tools for the incenter.

Investigation #1

Investigation #2


Student Activity


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