How do you calculate the scale factor between two similar shapes?

To calculate the scale factor between two similar shapes, the correct approach involves comparing the lengths of corresponding sides from each shape. The concept of similarity in geometry indicates that corresponding lengths maintain a consistent ratio across the shapes.

By taking the length of a corresponding side in one shape and dividing it by the length of the corresponding side in the other shape, you establish the scale factor, which represents the ratio of their linear dimensions. This ratio remains constant for all corresponding pairs of sides in similar shapes, ensuring a unified scale factor that can be applied throughout.

For example, if one triangle has a side measuring 4 units and the corresponding side of a similar triangle measures 2 units, the scale factor calculated would be 4/2 = 2. This indicates that the first triangle is twice as large in terms of its dimensions compared to the second.

The other methods for calculating the scale factor, like measuring the longest and shortest sides or calculating the perimeters, do not correctly capture the relationship needed to define the scale factor in terms of similarity between the two shapes. They may not produce consistent results across all corresponding sides, which is why the comparison of corresponding sides is the preferred method for determining the scale factor.