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# tetrahedron watch

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1. A regular tetrahedron has edge length 2 units. Find the distance from the midpoint of an edge to the midpoint of the opposite edge.

so a regular tetrahedron is made up of 4 identical equilateral triangles, made into a pyramid shape. Which length is it actually asking for. have looked at some diagrams of a tetrahedron and the midpoints of the edges don't seem to be opposite each other. thx
2. Imagine you are looking top down on the shape when it is flat on the floor. Pick an edge which is on the floor. Find the mid-point of that. From that mid-point, follow a line over the apex of the pyramid, and another edge should come down from the apex (this one doesn't run along the floor). The mid-point of that edge is your second point
3. I see, so basically start on the midpoint of one of the edges on the base, go up the flat face towards the apex, then down the straight edge half way. that sounds about right?
4. Yup
5. not seeing how to actually go about the problem. Can visualise the problem ok, but can't think how to find the direct distance from the edge to the edge. Can anyone give a helping hand please? thanks
6. Let the tetrahedron be ABCD, with midpoints M1 and M2 of the lines AD and BC respectively. Sketch the tetrahedron and the triangles ADB, DBM1, DBM2 and M1M2B. Should help you to visualise it.

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Updated: October 24, 2006
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