How to Construct Special Points in Triangles
In Geometry, you will frequently work with triangles. If you take advanced geometry classes, you will work with three special points in triangles: the circumcentre, the orthocentre and the centroid. The circumcenter is located at the intersection of the perpendicular bisectors of all three sides. The orthocenter is located at the intersection of the three possible altitudes of the triangle, and the centroid is located at the intersection of the medians of all three sides. Locating these points is not difficult, only requiring a ruler and a straightedge.
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Instructions
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1
Draw three lines that bisect, or cut in two, all three sides of the triangle. The line corresponding to a particular side of the triangle should form a 90-degree angle with the line when it bisects it.
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Locate the intersection of these line. This intersection is called the circumcentre.
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Treat each vertex of the triangle as a potential altitude. Drop a line straight down from each vertex, to the base of the triangle beneath.
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Find the intersection of these three altitudes. This intersection is called the orthocentre.
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Draw a line through the middle of each side of the triangle and out through the vertex opposite to the side. This is called drawing a line through the median of the side, and it will generally not form a 90-degree angle with the side, since you are drawing the line through the opposite vertex.
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Find the intersection of the three medians. This is called the centroid.
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