Answer:
The number of non-congruent triangles that can be formed by connecting 3 of the vertices of the cube is 3 non-congruent triangles
Explanation:
From the three dimensional shape of a cube, triangles can be constructed from;
1) 6 side faces
2) 4 front face to opposite vertices triangles
3) 4 rear face to opposite vertices triangles
Each face can produce ₄C₃ = 4 triangles
Therefore;
The total number of triangles that can be formed = 4 × 6 + 4 × 4 + 4 × 4 = 56 triangles
Of the 56 triangles, it will be found that all 24 triangles from the different 6 direct faces will have the same dimension of 1, 1, √2 are congruent
The 24 triangles formed by the sides of the faces and an adjacent diagonal have the same dimension of 1, √2, √3 and are congruent
The 8 triangles formed by joining the three diagonals have the same dimension of √2, √2, √2 are congruent
Therefore, the 56 triangles comprises of a combination of three non-congruent triangle.
There are only 3 observed non congruent triangles formed by connecting three of the vertices of the cube.