+0  
 
0
47
2
avatar+119 

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.

ANotSmartPerson  Oct 24, 2018
 #1
avatar+406 
+6

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.

KnockOut  Oct 25, 2018
 #2
avatar+119 
0

Ok, I'll try thank you.

ANotSmartPerson  Oct 26, 2018

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