Learning about Project Management while Proving Triangle Congruence

When you are learning the different congruence postulates for triangles, why just write them on the board?

Students in Mr. Borzi’s Honors Geometry class completed a much more hands-on project. The Academy’s covered walkway served as the testing ground for proving the different types of congruence. Armed only with sidewalk chalk, a yardstick, and a protractor, each student had to draw multiple triangles and prove the different postulates (Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, and Angle-Angle-Side). Students had total freedom in choosing where and how to draw their triangles. After drawing them, the students had the choice of measuring the different elements at that point or taking photos and then doing the measurements later.

Through the process of completing this project, students weren’t just learning about triangle congruence. Elements of the project itself were designed to help them develop real-world project management skills. For example, Mr. Borzi asked each student to provide time estimates of the steps they were going to use to create their triangles and how long they thought that would take. They then had to record the actual time the steps took and compare that information with their estimates. The students also had to overcome challenges based on environmental conditions and the materials they were using. Margo T. ‘22 observed that the thick chalk made the ruler move very slightly, which affected the angles and made her recalculate her measurements. In their reports about the project, they also had to note any potential accuracy issues and their causes. Since the real world is never a perfect “bubble” environment, this was a good opportunity for the students to adjust and adapt to any changes.  

Since the students’ triangle drawings are on the walkway that all students and faculty use to enter the school, their work has sparked interesting conversations. Each student signed their drawings so everyone knows who to talk to about each set of triangles. When asked about her drawings, Auden M. ‘21 said, “This is the best class ever!” It’s not every day that you hear that said about Geometry class but with a math teacher like Mr. Borzi, we would all be saying that!