Constructing the orthocenter of a triangle

Abstract:: An interactive applet and associated web page that provide step-by-step instructions on how to construct the orthocenter of a triangle using only a compass and straightedge. The method used involves constructing two altitudes of the triangle, which intersect at the orthocenter. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

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Euler line

Abstract:: An interactive applet and associated web page that describe the Euler line. It shows a triangle whose vertices can be dragged. As you drag them, the centroid, circumcenter and orthocenter move appropriately, showing that they are always collinear, always lying on the Euler line. There are controls to individually turn on the construction lines for each center. This helps visualize the concept since if they are all drawn at once, the diagram would be hopelessly confused. The web page has a full description the Euler line and has links to separate pages which go into each center in depth. Applet can be enlarged to full screen size for use with a classroom projector. Diagram can be printed. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Read the Fine Print

Abstract:: A web page and interactive applet demonstrating the concept of the orthocenter of a triangle. The applet shows a triangle where the user can drag the vertices around. The orthocenter and the altitude lines that generate it are continuously moved as the user drags the vertices. By experimentation the user can observe that the orthocenter can be inside or outside the triangle. The page text explains the definition of the orthocenter and how to find it. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.