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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)

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Solution Answer in seven | Comment 1 of 6
Bisect the obtuse angle, but stop before reaching the opposite side, and from that point draw four more lines, so the five lines form a star. These four lines will intersect the sides at four points, and two four sided figures will be formed. Draw their shorter diagonals, and you'll get seven acute triangels.
  Posted by Oskar on 2004-08-06 13:59:52
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