2009 AMC 8 Problem 20
Attempt Problem 20 of the 2009 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
How many non-congruent triangles have vertices at three of the eight points in the array shown below?
Answer: D
Small hint:
Use symmetry to avoid counting every triangle separately.
Big hint:
Classify triangles by their side lengths after choosing vertices from the two-row array.
Solution:
By symmetry, it is enough to list one representative of each possible triangle shape.
One complete list of non-congruent possibilities is and
Every other triangle formed from the eight points is congruent to one of these triangles.
Thus, D is the correct answer.
Problem 20 in other years
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