Question

a rectangular prism and rectangular pyramid are shown.
statements are given about the shape of the cross - section that would result from slicing the figures in different ways.
determine whether each statement about the resulting cross - section matches one or both of the figures shown.

	rectangular prism	rectangular pyramid
the cross - section for a slice parallel to the base would be congruent to the base.
the cross - section for slice parallel or perpendicular to the base could result in a shape with 4 sides.

Explanation:

Step 1: Analyze the first statement for Rectangular Prism

For a rectangular prism, slicing parallel to the base (which is a rectangle) will result in a cross - section that is also a rectangle, same shape as the base. So we check the box for Rectangular Prism.
For a rectangular pyramid, the base is a rectangle. Slicing parallel to the base, by the property of pyramids (similar figures), the cross - section will be a rectangle (same shape as the base, just smaller). So we check the box for Rectangular Pyramid.

Step 2: Analyze the first statement for Rectangular Pyramid

(Continued from Step 1, as the first statement analysis for pyramid is part of Step 1. Now Step 2: Analyze the second statement for Rectangular Prism)
For a rectangular prism, slicing parallel to the base, the cross - section is congruent to the base because the prism has uniform cross - section along its height. So we check the box for Rectangular Prism.
For a rectangular pyramid, slicing parallel to the base, the cross - section is similar to the base but not congruent (since the dimensions are scaled down as we move up the pyramid). So we do not check the box for Rectangular Pyramid.

Step 3: Analyze the second statement for Rectangular Pyramid

(Continued from Step 2, as the second statement analysis for pyramid is part of Step 2. Now Step 3: Analyze the third statement for Rectangular Prism)
For a rectangular prism, slicing parallel to the base gives a rectangle (4 - sided), slicing perpendicular to the base (along the height, parallel to the lateral faces) also gives a rectangle (4 - sided). So we check the box for Rectangular Prism.
For a rectangular pyramid, slicing parallel to the base gives a rectangle (4 - sided), slicing perpendicular to the base (through the apex and a side of the base) gives a triangle? No, wait, if we slice perpendicular to the base and parallel to a lateral edge, actually, if we slice a rectangular pyramid perpendicular to the base and through two opposite edges of the base, the cross - section is a triangle. But if we slice perpendicular to the base and parallel to a pair of opposite sides of the base, the cross - section can be a trapezoid (which is 4 - sided) or a triangle? Wait, no. Wait, the base is a rectangle. If we slice the rectangular pyramid with a plane parallel to the base, we get a rectangle (4 - sided). If we slice it with a plane perpendicular to the base and passing through the apex and a side of the base, we get a triangle. But if we slice it with a plane perpendicular to the base and parallel to one of the pairs of opposite sides of the base, the cross - section will be a trapezoid (which has 4 sides). So for the third statement, "The cross - section for slice parallel or perpendicular to the base could result in a shape with 4 sides", for the rectangular pyramid: slicing parallel to the base gives a 4 - sided figure, slicing perpendicular to the base (in a way that is parallel to a pair of opposite sides of the base) gives a 4 - sided figure (trapezoid). So we check the box for Rectangular Pyramid.

First Statement: "The cross - section for a slice parallel to the base would be the same shape as the base."

- Rectangular Prism: $\boxed{Checked}$
- Rectangular Pyramid: $\boxed{Checked}$

Second Statement: "The cross - section for a slice parallel to the base would be congruent to the base."

- Rectangular Prism: $\boxed{Checked}$
- Rectangular Pyramid: $\boxed{Unchecked}$

Third Statement: "The cross - section for slice parallel or perpendicular to the base could result in a shape with 4 sides."

- Rectangular Prism: $\boxed{Checked}$
- Rectangular Pyramid: $\boxed{Checked}$

(Note: Since the original problem has checkboxes, we are indicating the check status for each figure and each statement. If we were to represent the checkboxes as per the problem's table structure, for each row (statement) and column (figure), we mark if it's checked or not. But in the absence of the actual checkbox - marking interface, we describe the check status as above.)

Answer:

For the statement "The cross - section for a slice parallel to the base would be the same shape as the base":

• Rectangular Prism: Checked
• Rectangular Pyramid: Checked

For the statement "The cross - section for a slice parallel to the base would be congruent to the base":

• Rectangular Prism: Checked
• Rectangular Pyramid: Unchecked

For the statement "The cross - section for slice parallel or perpendicular to the base could result in a shape with 4 sides":

• Rectangular Prism: Checked
• Rectangular Pyramid: Checked

(If we were to fill the checkboxes in the table:

Statement	Rectangular Prism	Rectangular Pyramid
The cross - section for a slice parallel to the base would be congruent to the base.	$\boxed{\checkmark}$	$\boxed{\times}$
The cross - section for slice parallel or perpendicular to the base could result in a shape with 4 sides.	$\boxed{\checkmark}$	$\boxed{\checkmark}$	)