Which of the following cross sections are possible to get by slicing a right triangular prism with a plane? Select all that apply.
To determine which cross sections are possible to get by slicing a right triangular prism with a plane, we need to consider the different ways the plane can intersect the prism.
1. If the plane is parallel to the base of the prism, the cross section will be a rectangle.
2. If the plane is perpendicular to one of the lateral faces of the prism, the cross section will be a right triangle.
3. If the plane is perpendicular to the base of the prism, the cross section will be a right triangle.
Therefore, the possible cross sections that can be obtained by slicing a right triangular prism with a plane are a rectangle and a right triangle.
So, the correct answer is:
- Rectangle
- Right triangle
To determine which of the following cross sections are possible to get by slicing a right triangular prism with a plane, we need to consider the different possible orientations of the plane in relation to the prism.
A right triangular prism has two triangular faces and three rectangular faces. The orientation of the plane will determine the shape and size of the cross section.
1. Slice parallel to the triangular faces - In this case, the cross section will be a parallelogram.
2. Slice parallel to the rectangular faces - In this case, the cross section will be a rectangle.
3. Slice perpendicular to the triangular faces - In this case, the cross section will be a triangle.
4. Slice perpendicular to the rectangular faces - In this case, the cross section will be a rectangle.
Therefore, the possible cross sections are a parallelogram, rectangle, and triangle.