Japanese Geometry Problem Set #2

Here are this week's Geometry problems from Japan, again loosely scaffolded. They are getting juicier.

From doing/translating these problems, I have noticed that the Japanese expect a lot more from their students in terms of rigorously applying algebra to geometric settings. Check out the problem set and try out some of the non-guided problems, and you'll see what I mean. The problems are fun for me to do and to think about, because they're just one step up in terms of complexity from our normal Geometry problems in the States, even though the concepts involved are relatively few. Technically, all of the problems I've linked to thus far are just Pythagorean Theorem problems, with a couple of circle theorems and special right triangles tossed in here and there, but the way the problems are structured is significantly (far??) more complex than our typical American applications of the Pythagorean Theorem, requiring a fairly sophisticated understanding of algebra. It's amazing to think that this is what they expect from their public school children in middle school.

I hope you are enjoying these!