Author(s):

Vicente Meavilla Segui and Alfinio Flores

When students solve problems similar to the ones presented, the following contents of conceptual, procedural, or attitudinal nature can be introduced, firmed, or developed.

Conceptual contents

- Proportional magnitudes.
- Congruence and similarity of figures. Similarity ratio.
- Fourth proportional with respect to three line segments.

Procedural contents

- Identify the measure characteristics of similarity of plane figures in concrete situations.
- Apply similarity of figures to the solution of construction problems.
- Construction of the fourth proportional with respect to three line segments.
- Identification of similarity in plane figures.
- Search for relations in geometric figures and configurations.
- Construction of plane figures.

Attitudinal contents

- Value the usefulness of proportionality for the solution of problems.
- Skillful utilization of some drawing instruments (ruler, construction triangle, compass, computer programs…).
- Recognize and value the usefulness of
*regula falsi* for the solution of geometrical problems.
- Flexibility to solve geometric problems with different approaches.

In addition to the above benefits, the use of *regula falsi* can encourage teachers and students to experiment in mathematics. Experimenting in the context of similarity problems can lead to a better understanding. Discovery in mathematics is frequently preceded by multiple experiments.

Vicente Meavilla Segui and Alfinio Flores, "The Rule of False Position and Geometric Problems - Conclusions," *Convergence* (July 2010)