MHB Angle between two line segments of a cube.

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The angle between two diagonals drawn from a vertex of a cube is 60°, as they form an equilateral triangle with the vertex. This conclusion holds true when the diagonals are considered as those of the cube's face. The discussion clarifies that all three points involved (the vertex and the endpoints of the diagonals) lie in the same plane. Further applications can involve calculating angles and lengths of triangles formed in similar configurations. Understanding this geometric relationship can be useful for analyzing other line segments sharing a common point in three-dimensional shapes.
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Given a cube, choose a vertice and draw 2 of the three possible diagonals. What is the measure of the angel between those two diagonals?

Proposed answer: We can say that both diagonals touch vertice A, to give it a name. We can also call the endpoints of both diagonals B and C. If we imagine the diagonal that goes through points B and C, we can see that the points A, B, and C, all lie on the same plane and that they form an equilateral triangle. The measure of every angle in an equilateral triangle is 60°. The answer, I believe, is 60°.

Is this right? (Whether it is or isn't right, how can I apply this to any two line segments that share a point on the cube)
 
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It's correct, assuming "diagonal" means the diagonal of a face of the cube and the diagonals emanate from the chosen vertex. In order for me to answer the remaining question you'll have to be more specific about what application you are looking for. Do you mean finding the angles and lengths of triangles constructed in a similar fashion? By the way, any three points are contained in the same plane.
 
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