MathDB
Triangles

Source:

November 26, 2009
geometrycongruent triangles

Problem Statement

How many non-congruent triangles have vertices at three of the eight points in the array shown below? [asy]dot((0,0)); dot((0,.5)); dot((.5,0)); dot((.5,.5)); dot((1,0)); dot((1,.5)); dot((1.5,0)); dot((1.5,.5));[/asy] <spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 6<spanclass=latexbold>(C)</span> 7<spanclass=latexbold>(D)</span> 8<spanclass=latexbold>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 5 \qquad <span class='latex-bold'>(B)</span>\ 6 \qquad <span class='latex-bold'>(C)</span>\ 7 \qquad <span class='latex-bold'>(D)</span>\ 8 \qquad <span class='latex-bold'>(E)</span>\ 9