Tiffany N. KeysŐ Assignment 8:

Altitudes and Orthocenters

The orthocenter of a triangle is the common intersection of the three lines containing the altitudes. The orthocenter does not have to be on the segments that are altitudes, but can lie on the line extended along the altitude.

An altitude of a triangle is a perpendicular segment from any vertex to the line of the opposite side.

1.      Construct any triangle ABC.

2.      Construct the Orthocenter H of triangle ABC.

3.     Construct the Orthocenter A of triangle HBC.

4.    Construct the Orthocenter C of triangle HAB.

5.     Construct the Orthocenter B of triangle HAC.

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

OBSERVATIONS:

á     The altitudes of triangle ABC divided the triangle into three separate triangles.

á     All of the interior triangles are obtuse triangles.

á     The orthocenter of an interior triangle of the larger angle is coincident with the vertex of triangle ABC that is not on the interior triangle.

á     All of the circumcircles appear to be congruent .