Question

In order to receive full credit, you must explain your answer.
How does the net of a shoe box with no lid compares to the net of a shoe box with its lid on?
• A. Both the nets are identical.

B. The net of the shoe box with a lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the shoe box with no lid comprises six rectangles, three pairs of congruent rectangles.
C. The net of the shoe box with a lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the shoe box with no lid comprises six rectangles, three pairs of congruent rectangles.
D. The net of the shoe box with no lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the shoe box with its lid comprises six rectangles, three pairs of congruent rectangles.

Answer 1

To understand how the net of a shoe box with a lid compares to the net of a shoe box without a lid, let’s first clarify what a net is in this context. A net is a two-dimensional representation of a three-dimensional shape, created by laying out the surfaces of the shape flat.

For a typical shoe box, which is a rectangular prism, the net consists of the following surfaces:

1. **Shoe box with lid (closed)**:
- This shoe box has six surfaces: a top (the lid), a bottom, and four side walls.
- Therefore, the net of a shoe box with a lid will feature **six rectangles**—one for the top, one for the bottom, and four for the sides.

2. **Shoe box without lid (open)**:
- The shoe box without the lid has only five surfaces: a bottom and four side walls (it lacks the top).
- Thus, the net of a shoe box with no lid consists of **five rectangles**—one for the bottom and four for the sides.

Now, let’s analyze the answer choices:

- **Option A** states that both nets are identical, which we know is incorrect since the shoe box with a lid has six faces while the one without has five.

- **Option B** claims that both nets are different in terms of the number of rectangles and their congruence but does not accurately describe the number of rectangles for either box.

- **Option C** correctly identifies the shoe box with a lid as having five rectangles (which is incorrect) and incorrectly states the congruence.

- **Option D** accurately indicates that the net of the shoe box with no lid comprises five rectangles, including two pairs of congruent rectangles (the four side walls) and one odd rectangle (the bottom), while the shoe box with a lid indeed has six rectangles (which is not mentioned correctly in this option).

Considering this analysis, the only accurate distinction we can draw from the options given relates to their structure. The choice that accurately describes the properties of the nets is:

**B. The net of the shoe box with a lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the shoe box with no lid comprises six rectangles, three pairs of congruent rectangles.**

This option should reflect the correct attributes of the nets accurately. However, since this specific option is not directly available in your choices, I apologize for the previous classification; the correct answer deriving from the distinctions we established does not have proper representation among the provided options. Each statement carries misrepresented facts to some extent in terms of number and types of rectangle congruency.

As a summarized conclusion, the net of a shoe box without a lid combines five rectangles where two pairs are congruent forms from sides, while the box with the lid contains six rectangles in its net comprising four sides, one top, and one bottom. Thus, accurately depicting these properties enables better comparisons between both nets.