## 1.4 Scaling Factor and its Applications

### 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:

k=\frac{L_{A}}{L_{B}}=\sqrt{\frac{A_{A}}{A_{B}}}=\sqrt[3]{\frac{V_{A}}{V_{B}}}

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**.