Title
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
jtaylor1@rockdale.k12.ga.us
Link(s) to resources, references, lesson plans, and/or other
materials
