Question

a plane slices through a square pyramid perpendicular to its base and parallel to two sides of the base
what is the shape of the cross section?
the cross section is a
right triangle
parallelogram
square
isosceles triangle

Explanation:

Step1: Analyze the square pyramid and the plane's cut

A square pyramid has a square base and triangular faces. The plane cuts perpendicular to the base (so vertical, if base is horizontal) and parallel to two sides of the base.

Step2: Determine the cross - section shape

When we make such a cut, the cross - section will be a triangle. Since the plane is parallel to two sides of the square base and perpendicular to the base, the two equal - length sides of the triangle (from the two triangular faces of the pyramid that are cut) will be equal, so it's an isosceles triangle. A right triangle would require a right angle, but the cut here doesn't create a right angle. A parallelogram is not a triangle, and a square is not the shape here as the cut is through the triangular faces and the base's parallel sides don't create a square cross - section.

Answer:

isosceles triangle