# Suggested Enrichment Program Using Cinderella (DGS)

m_eldemerdash70@yahoo.com

## Enrichment Program Activities

### Activity 4: Animating and Tracing Loci Facilities of Cinderella

#### Other Geometric Loci Related to triangle

• ##### The Locus of the Intersection Point of Perpendicular Bisectors of the Sides of a Triangle

Furthermore, the situation can be elaborated to discover and generate other loci by considering the intersection point of two different lines in the triangle such as the intersection point of a height and a median, the intersection point of a median and a perpendicular bisector, etc.

The below table is used to organize the situations design with a notice that the line in the header of the table is the line, which moves through the movable vertex (the vertex C).

 Height (H) Median (M) Angular Bisector (A. B.) Height (H) Heights inter. point M + H A. B. + H Median (M) H + M Medians inter. point A. B. + M Angular Bisector (A. B.) H + A. B. M + A. B A. Bisectors inter. point Perpendicular Bisector (P. B.) Height + P. B. M + P. B. A. B. + P. B.

The situation can be further elaborated to discover and generate other interesting loci related to the triangle, if we construct the two intersecting lines of the triangle so that they do not pass through the movable vertex.

The following table should help a lot in organizing the situations design.

 Height (H) Perpendicular Bisector (P. B.) Median (M) Angular Bisector (A. B.) H +A. B. P. B. + A. B. M + A. B. Height (H) P. B. + H M + H Perpendicular Bisector (P. B.) M + P. B.