Jernita Randolph

Altitudes and Orthocenters

1. Construct any triangle ABC.

2. Construct the Orthocenter H of triangle ABC.

3. Construct the Orthocenter of triangle HBC.

4. Construct the Orthocenter of triangle HAB.

5. Construct the Orthocenter of triangle HAC.

6. Construct the Circumcircles of triangles ABC, HBC, HAB, and HAC.

It appears that all of the circles are congruent. If you move any of the vertices to the orthocenter (H), that vertex and H will switch positions.

GSP sketch

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