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jmc

geometry junior

Problem

Any three vertices of the cube , shown in the figure below, can be connected to form a triangle. (For example, vertices , , and can be connected to form isosceles .) How many of these triangles are equilateral and contain as a vertex?
problem
(A)
(B)
(C)
(D)
Solution
The only equilateral triangles that can be formed are through the diagonals of the faces of the square. From P you have possible vertices that are possible to form a diagonal through one of the faces. Therefore, there are possible triangles. So the answer is
Final answer
D