Triangle
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The triangular pyramid has four faces, one of them being the base. Since the slicing plane doesn't intersect the base or run parallel to it, it must intersect the other three triangular faces of the pyramid. Because it intersects each face and each face is a triangle, the intersection with each face will be a line segment.
These line segments are connected since the faces of the pyramid are connected. The only closed shape that can be formed by three straight line segments is a triangle.
Therefore, the most precise name for the shape of the cross section is a triangle.
