Similar Figures and Shapes
Two shapes are similar if they share the same shape but not the size.
- Their corresponding angles are equal;
- Their corresponding sides are in the same ratio.
Calculating the Scaling Factor
- The scaling factor is a numerical value representing the scale of one shape/object to a similar shape (with a different scale).
- The scaling factor can be calculated as the proportional difference between the lengths of the two shapes/objects, the square root of the proportional difference between their areas, or the cubic root of the proportional difference between their volumes:
Note: this calculates the scaling factor for shape/object A with respect to shape/object B. For example, a scaling factor of 2 means A has twice the length of B.
- The scaling factor is dimensionless (i.e. has no units).
- k>0The scaling factor is larger than 0.