Cylinder
Triangular
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).
Parallel
Both, a cylinder and a prism have two faces (bases) at either end. These are parallel and identical. A plane that is parallel to these bases will cut the cylinder (or prism) in identical cross sections.
false
A sphere is.
A square pyramid is.
That's a statement that can apply to any rectangular prism.
The bases of a prism or cylinder are congruent and parallel and they meet the lateral face (cynder) or faces (prism) at right angles. A cross section parallel to the longitudinal axis will, therefore, be a rectangle.
cone and prism
All cross sections of a square pyramid that are parallel to the base are squares
True
True
In a standard cylinder, all horizontal cross-sections are congruent circles regardless of the height at which the cut is made. If the statement asserts that the cross-sections are not all congruent, it suggests that the figure in question may not be a true cylinder. Instead, it could be a shape that varies in diameter along its height, such as a tapered or irregular prism.
The answer depends on the angle at which the axis of the cone intersects the cross-sections.
A solid that has congruent horizontal and vertical cross sections is a cylinder. In a cylinder, both the horizontal cross sections (circles) and vertical cross sections (rectangles) maintain consistent dimensions throughout the solid. This property ensures that the shapes formed by slicing the cylinder in any horizontal or vertical plane are always congruent to each other. Other examples include cubes and spheres, but the cylinder specifically illustrates this characteristic well.
The horizontal cross-sections of a cone are circular in shape, and these circles are congruent to each other at all heights except for the vertex, which is a single point. As you move away from the vertex along the height of the cone, the diameter of the circular cross-sections increases uniformly. This consistent shape results in a series of congruent circles, illustrating the cone's geometric properties.