ambidextrous tetrahedrons

Congruence versus Chirality

As math teachers, we tend to spend a lot of time with congruence. Two triangles are congruent if and only if they may be superimposed on one another. Part for part, angle for angle they match up.

Rather than translate the triangles (i.e. moving them), we have those theorems all trig students learn: SAS, SSS, ASA, AAS and HL. If two sides and an included angle are the same, the two triangles are congruent. Ditto if…