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“Given a triangle with one obtuse angle, is it possible to cut the triangle into smaller triangles, all of them acute?” Isn't the answer obviously 'yes'? Am I
by SteveWatson 11y ago
“Given a triangle with one obtuse angle, is it possible to cut the triangle into smaller triangles, all of them acute?”
Isn't the answer obviously 'yes'? Am I missing something?
- 3JPLW 11y agoIt is possible, but I wouldn't consider it trivial. Given an obtuse triangle with vertices A, B, and C, where vertex C is the obtuse angle, one of the dissection lines must split vertex C in order to make two acute angles. Now, you have some choices as to where this line goes. If it is simply dissected straight across to the line segment AB, then you can either form two right triangles, or one acute and one obtuse. Either way, you're right back where you started, needing to segment a non-acute triangle into acutes. So that can't be the solution. This means that the new segment starting from C must terminate at a new point D in the interior of the triangle...