Question

Suppose a cube is given.

Answer 1

Answer:

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

Step-by-step 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.