Special Points of a Triangle

Special Points of a
Triangle
Centroid, Circumcenter,
Incenter, Orthocenter
Centroid
The point of intersection of the medians of a triangle.
Problem: Draw a triangle with its centroid.
Select F2 Triangle. Draw a triangle.
Select F3 Midpoint. Draw a midpoint on each side.
Select F2 Segment. Connect each midpoint to its opposite vertex.
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©2003 Jerry Cummins

Select F2 Point, cursor to Intersection. Place a point at the intersection of the
medians.
Select F5 Hide/Show, cursor to Objects. Hide the segments.
Select F5 Alph-num. Label the centroid CT.
Select F3 Hide/Show Objects Hide the centroid and the midpoints.
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©2003 Jerry Cummins

Circumcenter
The point of intersection of the perpendicular bisectors of the sides of a triangle.
Problem: Draw a triangle with its circumcenter.
Use the triangle above. Select F3 Perp. Bis. Draw the perpendicular bisectors of
the sides of the triangle.
Select F2 Point, Intersection. Place a point at the intersection.
Select F5 Hide/Show, Objects. Hide the lines.
Select F5 Alph-num. Label the point CC.
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©2003 Jerry Cummins

Select F5 Hide/Show, Objects. Hide the circumcenter.
Incenter
The point of intersection of the angle bisectors of a triangle.
Problem: Draw a triangle with its incenter.
Use the triangle above. Select F3 Angle Bis. Draw the angle bisectors. Select 3
vertices to draw an angle bisector.
Select F2 Point, Intersection. Place a point at the intersection.
Select F5 Hide/Show, Objects. Hide the lines.
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©2003 Jerry Cummins

Select F5 Alph-num. Label the point IN.
Select F5 Hide/Show, Objects. Hide the Incenter.
Orthocenter
The point of intersection of the altitudes of a triangle.
Problem: Draw a triangle with its orthocenter.
Use the triangle above. Select F3 Perp. Draw the altitudes to each side or
extended side of the triangle. You need to select a vertex and the side opposite
the vertex to draw the perpendicular. You can select the side first, then the vertex
or vice versa.
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©2003 Jerry Cummins

Select F2 Point, Intersection. Place a point at the intersection.
Select F5 Hide/Show, Objects. Hide the lines.
Select F5 Alpha-num. Label the Orthocenter OC.
Select F5 Hide/Show, Objecta. Show all four special points of the triangle.
Problem: Grab a vertex with the hand (ALPHA). Move the point and make conjectures
that describe relationships of the points to each other and to the triangle.
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©2003 Jerry Cummins

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©2003 Jerry Cummins