Formulas for special segments in a triangle

Fraivert, David and Stupel, Moshe (2018) Formulas for special segments in a triangle. At Right Angles, 7 (2). pp. 72-85.

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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.

Item Type: Articles in APF Magazines
Authors: Fraivert, David and Stupel, Moshe
Document Language:
Uncontrolled Keywords: Formula development, Relationship formulas in the triangle, Algebraic Identities, Characteristics of isosceles triangles, Heron’s formula, Nonlinear systems.
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University Publications > At Right Angles
Full Text Status: Public
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