Further, the teacher should assist students in the utilization of the geometry package which the students will use to form and test their various conjectures. Likewise, the teacher should encourage the students to work cooperatively to develop and test their conjectures and explanations. Students should be know the difference among altitude, median, and perpendicular bisector. Students need to be able to recognize similar triangles and their proportions between them. After calculating each type of mean, the teacher might want to review the various parts of a right triangle to insure that all students are utilizing their correct mathematical vocabulary skills.
Students often have a difficult a difficult time with the geometric means and right triangles.
One of the many goals of this lesson is to allow the students to use a dynamic geometry program such as Geometer's Sketchpad or Cabri Geometry to investigate the various relationships which occur among the lengths of different pieces of the right triangles. Name each of the them. Compare the interior angle measures of the three triangles. List the congruent angles. Write a statement showing the relationship among the three triangles.