To identify the scale factor between the two triangles, we compare corresponding sides of the two triangles. The given triangles are right triangles, and their sides are labeled as follows:

• Small triangle: Two sides are labeled as 4 and 4 units.
• Large triangle: Two corresponding sides are labeled as 8 and 8 units.

To find the scale factor, we can divide the length of a side of the larger triangle by the corresponding side of the smaller triangle. For example:

$\text{Scale factor} = \frac{\text{side of large triangle}}{\text{side of small triangle}} = \frac{8}{4} = 2$

Thus, the scale factor is 2. This means the larger triangle is twice as big as the smaller triangle.

Would you like more details or have any questions about this?

Here are 5 related questions to expand on this:

1. How do you verify that the triangles are similar?
2. What is the significance of corresponding angles in similar triangles?
3. If one side of the smaller triangle was 5, what would the corresponding side length of the larger triangle be with the same scale factor?
4. How does the concept of scale factor apply to area and perimeter?
5. Can the scale factor ever be a decimal or fraction? In what cases?

Tip: Always ensure that you match corresponding sides or angles when calculating scale factors or working with similar shapes.