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avatar+183 

How many different non-congruent isosceles triangles can be formed by connecting three of the dots in a 4x4 square array of dots like the one shown below?

*   *   *   *
*   *   *   *

*   *   *   *

*   *   *   *

 

Two triangles are congruent if they have the same traced outline, possibly up to rotating and flipping. This is equivalent to having the same set of 3 side lengths. 

 

The answer is not 9 or 3.

 Oct 24, 2018
 #1
avatar+624 
+13

I'm not sure. I've done the same exact problem somewhere else before, but I do not recall the answer.

 

Here is a similar question: https://artofproblemsolving.com/wiki/index.php?title=2009_AMC_8_Problems/Problem_20

 

Maybe like the question above, sort them by base lengths, and see how many triangles can be formed by connecting points from each distinct base length.

 Oct 25, 2018
 #2
avatar+183 
0

Ok, I'll try thank you.

 Oct 26, 2018

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