Fraivert, David and Stupel, Moshe
(2018)
Formulas for special segments in a triangle.
At Right Angles, 7 (2).
pp. 72-85.
Abstract
In many programs of study, the material on the formulas relating the sides and special segments in a triangle
does not appear as part of the study of mathematics in high school. On the other hand, in many programs
of study the background required to understand this subject is studied already by the ages of 13-15. This
situation gives us the opportunity to teach the relationship formulas at an early stage, even before the studies
of geometry have begun in the precise manner at the higher level of difficulty.
In this paper we propose a structure and a method for teaching the relationship formulas that has been
tried with a group of students. Teaching the relationship formulas by this manner will present the students
with many uses for material that has already been studied, and will expose them to new methods for solving
problems in geometry and algebra.
This paper presents material that is suitable for students aged 13-15. The material includes: (1) Obtaining three
formulas that relate special segments in the triangle to the sides of the triangle; (2) Using these formulas for
proving three geometrical theorems; (3) Examples of problems in geometry that can be solved algebraically
using these formulas; (4) Didactic recommendations for teaching this material.
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