[size=100][center][/center][/size][size=150]For reference, above are two congruent Taxicab triangles.[/size]
Lesson 8
[b]We've talked about distance, we've talked about circles and squares, but what about triangles? Triangles start get a little bit complicated in Taxicab geometry, but we'll start easy. Below is a Euclidean triangle, and some examples of what Taxicab triangles look like, and their geometric properties. Remember the congruency rules for triangles we've talked about previously: SAS, SSS, AAS. [/b]
Below is a euclidean triangle. We can move the triangle and it stays congruent, no matter how we move it.
[size=150]Above can see two triangles, which satisfy Side-Angle-Side-Angle-Side, but are not congruent.[/size]
[size=200][size=150]Here, again, we see two triangles. This time, the two triangles are not congruent in either context, even though they follow SSS rule for the taxicab triangles. [/size][/size]
Using the empty geogebra applet, create some taxicab triangles of your own. Remembering what we know about congruency rules in the Euclidean plane (SSS, SAS, etc), What holds true in the Taxicab plane? What doesn't? Create some taxicab triangles that are congruent, and some that aren't.
What makes the Euclidean triangles similar in the third image? Do the Taxicab triangles also follow this rule, even though they are not congruent? at are your thoughts about congruency and similarity in the Euclidean plane vs. the Taxicab plane?
What congruency rule must Taxicab triangles follow to definitely be congruent?