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UKMT Senior Mathematical Challenge, 2018

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A regular tetrahedron is a polyhedron with four faces, each of which is an equilateral triangle, as shown. A solid regular tetrahedron is cut into two pieces by a single plane cut. Which of the following could not be the shape of the section formed by the cut?

(A) a pentagon (B) a square (C) a rectangle that is not a square (D) a trapezium (E) a triangle that is not equilateral

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