A pyramid has cross-sectional shapes, taken parallel to its base, that are to one another.
A. similar
B. equal
C. equivalent
D. congruent
Answer (2)
Cross-sectional shapes of a pyramid taken parallel to its base have the same shape as the base.
The size of the cross-section changes depending on the distance from the base.
Cross-sections with the same shape but different sizes are similar.
The cross-sectional shapes are similar to one another: A .
Explanation
Analyze the problem Let's analyze the properties of cross-sections of pyramids parallel to the base. When a plane intersects a pyramid parallel to its base, the cross-section is a polygon that has the same shape as the base. However, the size of the polygon changes depending on the distance from the base.
Determine the relationship between cross-sections Since the cross-sections have the same shape but different sizes, they are similar to one another.
Select the correct answer Therefore, the correct answer is A. similar.
Examples
Imagine you're slicing a cake shaped like a pyramid. Each slice you make parallel to the base will have the same shape as the base, but the size of the slice will vary depending on where you cut the cake. This is similar to how cross-sections of a pyramid behave; they are all similar shapes but can be different sizes.
The cross-sectional shapes of a pyramid taken parallel to its base are similar to one another. They maintain the same shape but vary in size, making option A: similar the correct choice. This similarity is due to their consistent proportions to the base across different heights of the pyramid.
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