A scale factor is a number that scales, or multiplies, the dimensions of a figure to create a similar figure. It represents the ratio of corresponding sides between two similar geometric shapes, such as triangles, rectangles, or polygons. If you have two figures, the scale factor describes how much larger or smaller one figure is compared to the other.

Key Points:

1. Enlargement: If the scale factor is greater than 1, the figure is enlarged (the new shape is larger).
2. Reduction: If the scale factor is between 0 and 1, the figure is reduced (the new shape is smaller).
3. Proportionality: Corresponding angles between the two figures remain the same, while the sides are proportional by the scale factor.
4. Linear dimensions: The scale factor applies to linear dimensions, such as length, width, and height.
5. Area and Volume: When scaling a figure, the area changes by the square of the scale factor, and the volume changes by the cube of the scale factor.

For example:

• If a rectangle with sides 4 cm and 6 cm is scaled by a factor of 2, the new rectangle will have sides 8 cm and 12 cm.

Would you like to explore more details about scale factors or have a specific example? Here are some follow-up questions that might be useful:

1. How do you find the scale factor between two shapes?
2. What happens to the area when you apply a scale factor?
3. How does volume change when you scale a three-dimensional shape?
4. What is the difference between similar and congruent shapes in terms of scale factor?
5. Can you apply a scale factor to real-life objects like maps or models?

Tip: When scaling shapes, remember that perimeter scales directly by the factor, but area scales by the square of the factor!