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Suppose a cube is given.

How many non-congruent triangles can be formed by connecting 3 of the vertices of the cube?

User Liqang Liu
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Answer:

The number of non-congruent triangles that can be formed from the vertices of a cube are 3 triangles

Explanation:

The number of non congruent triangles that can be formed by connecting 3 of thee vertices of the cube is found as follows;

The available different lengths of segments joining two vertices of a cube of side length s = 2 are;

2, 2·√2, and 2·√3

Therefore, since there are only three different side lengths we have the possible triangle dimensions given as follows

Distinct triangle one = 2, 2, 2·√2

Distinct triangle two = 2·√2, 2·√2, 2·√2

Distinct triangle three = 2, 2·√3, 2·√2

Therefore, there are ₃C₃ = 3 ways of forming three non-congruent triangles from the vertices of a cube.

User Brendanator
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