Chapter 9
Triangle Centers and Constructions
Imagine cutting a triangle from a sheet of stiff paper and trying to balance it on one fingertip. Where would you place your finger? The middle is easy to picture in a circle, but a triangle has corners and sides that can suggest different choices. Triangle centers give us a way to explore what a center might mean for this shape. How could careful geometric constructions help us choose a point without relying on a guess?
What You'll Explore
4 lessons.
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Where could you place a point so that it is equally far from the two ends of a segment? Explore this question with geometric constructions, then consider the challenge of choosing a point equally far from all three corners of a triangle.
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Can a point inside an angle be equally far from both sides? Investigate what distance means in this setting and how the question changes when you consider the three sides of a triangle instead of its corners.
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Suppose you want to balance a triangle cut from a uniform sheet of cardboard. Investigate whether lines drawn through its corners can help you locate a balancing point, and what patterns appear when you compare the segments they create.
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How might changing a triangle's shape change the picture formed by its altitudes? Explore different kinds of triangles, then compare all four triangle centers and consider whether they can ever share the same location.