6.6 Congruence (Basic Mathematics)

Having seen all the possible isometries, let's finish up with a definition of congruence. Two sets of points are congruent if there exists an isometry that can map one to the other.

Thank you!

[callmedeno]

This isometry section officially kicked my ass, I couldn't come up with almost any of the proofs. It's my first foray into geometry, I thought I'd be better at it than algebra because the visual elements would aid intuition but I found in trying to do geometry proofs, visual intuition clouded the logic more than anything. By the last couple of exercises I had to hold up the white flag for the first time.

When I finally did give up and look at solutions, I feel I didn't have enough in the toolbox to even come close to solving some of them. Although I know they weren't, some of the leaps seemed almost arbitrary compared to previous proofs. In the beginning of the chapter up to about theorem 3 to 6, although I didn't get the proofs myself I could follow the logic. Became much more fuzzy in the later sections, where you just say 'there is an isometry that that takes the first triangle vertex to another, so let's assume that case. Then you do it again for the second vertex. And then the last vertex is a reflection etc. Ultimately I know each theorem quite well now, but shocked by my lack of creativity, proof-writing here.

[gokhanerylmaz]

Your videos are very helpful after reading the book but not understand the topics well enough. Thanks very much.

[kal]

Revisiting this text, thanks for doing this video --- congruence is an important subject, but I never explored it to this depth.