Intermath | Workshop Support


Classified Information

Problem Statement
Triangles can be classified by their side lengths (scalene, isosceles, and equilateral), and by their angle measure (acute, right, and obtuse). However, not all combinations of these classifications exist.

Does each of the following triangles exist? If yes, draw the triangle accurately, with measurements. If no, explain why it cannot exist.

                         a right isosceles triangle

                         a right equilateral triangle

                         a right scalene triangle

                         an acute scalene triangle

                         an acute isosceles triangle

                         an acute equilateral triangle

                         an obtuse scalene triangle

                         an obtuse isosceles triangle

                         an obtuse equilateral triangle

Problem setup

The challenge is to create each triangle according to dual definitions, or to prove that it is impossible to create them. I plan to create an example of each type in GeoSketchPad, or give the reason in GeoSketchPad why it was impossible to create.


Plans to Solve/Investigate the Problem

I created an example of each type in GeoSketchPad. I identified the angle and side measurements to ensure accuracy.


Investigation/Exploration of the Problem

I was able to construct all of the triangles with the exception of 2: the Right Equilateral and the Obtuse Equilateral. My GeoSketchpad Drawings and explanations are shown below:








Author & Contact
Jim Taylor

Link(s) to resources, references, lesson plans, and/or other materials