Final answer:
The rule of proportionality for a 3D pyramid in geometry dictates that dimensions must change consistently to maintain the same shape. The change in height is proportional to the original height, and this principle is used in scaling the pyramid's size while preserving its proportions.
Step-by-step explanation:
The rule of proportionality in geometry, specifically for a 3D pyramid, is based on the concept that if the dimensions of a pyramid are changed proportionally, the new dimensions of the pyramid will still maintain the same shape. This is expressed in the change in height being proportional to the original height. For instance, if the original height of one pyramid (Block B) is twice that of another pyramid (Block A), then any changes made to the height of Block B will be twice the changes made to Block A to maintain the same proportions. This principle is applicable across all dimensions of the pyramid and is essential in scale transformations.
For example, referencing the moon, the width observed from a point (KD = x), leads us to determine that the visible angle is consistent due to the congruence of the triangles involved. Thus, if we know a linear dimension and the scale factor, we can find the corresponding dimension in the model or the actual subject. In essence, mathematical ratios and proportionality are used to maintain the general proportions in scaling the dimensions of objects like buildings, distances, and even in the field of art for creating lifelike sculptures.