Gizmo of the Week: Concurrent Lines, Medians, and Altitudes

The Concurrent Lines, Medians, and Altitudes Gizmo shows four ways of dividing a triangle: by perpendicular bisectors, angle bisectors, altitudes, and medians. Students can select each type of bisector, use rulers and protractors to measure lengths and distances, and manipulate the vertices of a triangle to see that—no matter what triangle is used—each of these sets of lines converge at a point. A variety of observations can be made about each of these lines: how the circumcenter relates to the circumscribed circle, the incenter to the inscribed circle, and the location of the orthocenter to the type of triangle. The lesson concludes with an extension on the mysterious Euler line that links the circumcenter, orthocenter, and centroid.

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