by Brad Simmons
Use geometer's sketchpad to construct the orthocenter of a triangle.
The lines containing the altitudes of a triangle all pass through a common point. These lines are said to be concurrent. The point of concurrency of these altitudes is called the orthocenter of the triangle.
1. Start with triangle ABC.
2. Construct the three altitudes of triangle ABC. An altitude is a line that passes through a vertex of the triangle and is perpendicular to the side of the triangle opposite of said vertex.
3. Construct the point of intersection of these three altitudes. This point of concurrency is the orthocenter and is typically named point H.
Please click here for a geometer's sketchpad sketch that can be manipulated.
Use geometer's sketchpad to construct the orthocenter for each triangle shown below.