2009 AMC 8 Problems/Problem 20
Problem
How many non-congruent triangles have vertices at three of the eight points in the array shown below?
Solution
Assume the base of the triangle is on the bottom four points because a congruent triangle can be made by reflecting the base on the top four points. For a triangle with a base of length , there are triangles. For a triangle with a base of length , there are triangles. For length , there are . In total, the number of non-congruent triangles is .
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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