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Question
Prove that the tetrahedron with vertices at the points O(0, 0, 0), A(0, 1, 1), B(1, 0, 1) and C(1, 1, 0) is a regular one.
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Solution
The faces of a regular tetrahedron are equilateral triangles.
Let us consider\[\bigtriangleup\]
\[OA = \sqrt{\left( 0 - 0 \right)^2 + \left( 0 - 1 \right)^2 + \left( 0 - 1 \right)^2}\]
\[ = \sqrt{2}\]
\[ = \sqrt{2}\]
\[ = \sqrt{2}\]
Similarly,\[\bigtriangleup\]OBC,\[\bigtriangleup\]OAC,
Hence, the tetrahedron is a regular one.
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