Triangular
congruent
It depends on the angle of the plane of the cross section. If it is parallel to the cube's face (or equivalently, two adjacent edges) the cross section will be a square congruent to the face. If the plane is parallel to just one edge (and so angled to a face), the cross section will be a rectangle which will have a constant width. Its length will increase, remain at a maximum level and then decrease. If neither, it will be a hexagon-triangle-hexagon-triangle-hexagon (triangles when passing through a vertex).
You cannot have a 2d cylinder. The 2d cross section will depend on the plane of the cross section.
It can be a square, a trapezium, a quadrilateral or a triangle - depending on the inclination of the plane which defines the cross section.
That conic section is a circle.When you slice a cone with a plane parallel to the base of the cone, the sliced section is a circle, and the portion of the original cone on the side of the vertex is again a cone.An isosceles cone would be the out come
Parallelogram
You cannot have a 2d prism. The 2d cross section will depend on the plane of the cross section.
Sphere
Only if the section is taken by a plane parallel to one of the faces.
Then the cross-section is a circle or a point.
It creates a triangular frustum.
It depends on the angle of the plane of the cross section. If it is parallel to the cube's face (or equivalently, two adjacent edges) the cross section will be a square congruent to the face. If the plane is parallel to just one edge (and so angled to a face), the cross section will be a rectangle which will have a constant width. Its length will increase, remain at a maximum level and then decrease. If neither, it will be a hexagon-triangle-hexagon-triangle-hexagon (triangles when passing through a vertex).
It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.
A rectangle.
It is a horizontal cross-section. Its shape will depend on the shape of the solid and its orientation.
No.When they are on different planes and they do not cross, they are called skew lines, they are not considered parallel. When they ARE parallel, it means that they do not cross and they both lie on ONE plane
never
If your question is "What is the cross-section of the intersection?" then the answer is "A circle." Otherwise, I can't make sense of the question.