Watch and learn how to determine the scale factor between a pair of similar figures.

# Determining The Scale Factor Of Similar Figures

To determine the scale factor between two similar triangles, you can compare the corresponding sides of the triangles.

Given two similar triangles \(A\) and \(B\):

1. Identify Corresponding Sides: First, identify corresponding sides between the two triangles. In similar triangles, corresponding sides are proportional.

2. Calculate Scale Factor: To find the scale factor from \(A\) to \(B\), divide the length of a corresponding side of triangle \(B\) by the length of the corresponding side of triangle \(A\). Similarly, to find the scale factor from \(B\) to \(A\), divide the length of a corresponding side of triangle \(A\) by the length of the corresponding side of triangle \(B\).

Let's apply these steps to the given triangles:

Triangle \(A\):

- Height = 4

- Base = 8

Triangle \(B\):

- Height = 3

- Base = 6

To find the scale factor from \(A\) to \(B\):

- Compare the height of \(B\) to the height of \(A\): \(3 \div 4 = 0.75\)

- Compare the base of \(B\) to the base of \(A\): \(6 \div 8 = 0.75\)

So, the scale factor from \(A\) to \(B\) is \(0.75\), which means that the corresponding sides of triangle \(B\) are \(0.75\) times the length of the corresponding sides of triangle \(A\).

To find the scale factor from \(B\) to \(A\):

- Compare the height of \(A\) to the height of \(B\): \(4 \div 3 = 1.33\)

- Compare the base of \(A\) to the base of \(B\): \(8 \div 6 = 1.33\)

So, the scale factor from \(B\) to \(A\) is \(1.33\), which means that the corresponding sides of triangle \(A\) are \(1.33\) times the length of the corresponding sides of triangle \(B\).

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