Angles in a Cube II

Let denote the vertices of a cube ABCD (for the bottom face) and A'B'C'D' (for the top face), with A' above A, etc. Let K, L, M denote the midpoints of A'B', B'C' and CC'. What is the angle KLM?


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Solution

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Solution

Check the "6 segments" box. You'll see a hexagon with all sides equal and clearly all angles also equal as they may be overlayed by rotating the cube.


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

The applet helps verify that the hexagon is planar: all its vertices lie in the same plane, implying that the hexagon is regular, so that the angle in question is 120°.


Related material
Read more...

  • Angles in a Cube I
  • Angles in a Cube III
  • Bimedians in a Regular Tetrahedron
  • Cut the Cone
  • Cut the Cube
  • Cut the Cylinder
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    Copyright © 1996-2017 Alexander Bogomolny

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