Triangle Properties in Taxicab Geometry
We know a lot about triangles in Euclidean geometry. When studying Taxicab geometry a natural question arises, do these properties still hold in the Taxicab universe?
Use the applet below to play around with some triangles and conjecture whether properties that you know about Euclidean triangles still apply to Taxicab triangles.
For instance you might explore:
- Do isosceles triangles always have two congruent angles?
- Is the sum of two sides of a triangle always greater than the third?
- Does the Pythagorean theorem still hold?
What did you learn from your exploration?