To determine the characteristics of the cross-sections created by planes in right rectangular pyramids (Figure 1 and Figure 2), we need to consider how cutting through these shapes at various angles impacts the resulting cross-section.
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Right Rectangular Pyramid: When a plane intersects through the height of a right rectangular pyramid, the resulting cross-section can vary based on the angle and position where it cuts through the shape.
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Vertical Sections: If the plane cuts vertically through the apex (the top point) and base (the rectangular base), the cross-section will be a triangle.
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Horizontal Sections: Conversely, if the plane cuts parallel to the base, the cross-section will typically be a rectangle, assuming it is cut at a height that doesn't reach the apex.
Given these explanations, we analyze the provided options:
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A and B can be excluded because they describe cross-sections that are uniformly rectangles or parallelograms, which doesn't account for variations expected from planes passing through pyramids in different orientations.
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C mentions that the cross-section of Figure 1 is a triangle (which is possible if it cuts through the apex) and Figure 2 is a rectangle (if it cuts horizontally through the base). This is a plausible statement since both scenarios align with potential cross-section outcomes.
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D reverses the roles of the cross-sections for Figure 1 and Figure 2 but remains within possible configurations of cutting through the pyramids.
Without more specific information about which way the planes are cutting through each pyramid, I can't definitively state which one is correct. However, if uniformly cutting through one pyramid vertically and another horizontally, C seems a more probable option, assuming Figure 1 is cut to form a triangle from the apex and Figure 2 is cut parallel to the base to form a rectangle.
Thus, C is the best answer: "The cross-section of Figure 1 is a triangle, and the cross-section of Figure 2 is a rectangle."
1 answer