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A Cute Dissection (Posted on 2004-08-06) Difficulty: 4 of 5

How can you guarantee that you can cut an obtuse triangle into smaller triangles, all of which are acute? An obtuse triangle is a triangle with one obtuse angle. An acute triangle is a triangle with three acute angles. A right angle is neither acute nor obtuse. If you can find such a dissection, what is the smallest number of acute triangles into which any obtuse triangle can be dissected?

The graphic shows how this obtuse triangle can be divided into almost all acute triangles except one - the blue one. What approach should be used when one must cut an obtuse triangle into acute triangles only?

No Solution Yet Submitted by SilverKnight    
Rating: 2.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts You can't get six this way... Comment 6 of 6 |
(In reply to I get six! Vehe! by Vee-Liem Veefessional)

Your quadrilateral has four angles at the center -- at least ONE of those angles must be 90 degrees or greater.
  Posted by Federico Kereki on 2004-08-08 08:49:53

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