Problem:
Consider the figure consisting of a square, its diagonals, and the segments joining the midpoints of opposite sides. The total number of triangles of any size in the figure is
Answer Choices:
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Solution:
Since all the acute angles in the figure measure , all the triangles must be isosceles right triangles. It follows that all the triangles must enclose one, two or four of the eight small triangular regions. Besides the eight small triangles, there are four triangles that enclose two of the small triangular regions and four triangles that enclose four, making a total of .