The scale factor of similar triangles is the ratio of corresponding side lengths of the two triangles.
In essence, similar triangles have the same shape but different sizes. This means their corresponding angles are equal, and their corresponding sides are proportional. The scale factor is the number you multiply the side length of one triangle by to get the corresponding side length of the other triangle.
Understanding Scale Factor
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Definition: The scale factor is the ratio between corresponding lengths in similar figures.
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Calculation: To find the scale factor, divide the length of a side in the "new" triangle (the image) by the length of the corresponding side in the "original" triangle (the pre-image).
Scale Factor = (Length of side in new triangle) / (Length of corresponding side in original triangle) -
Implications:
- If the scale factor is greater than 1, the new triangle is larger than the original triangle (an enlargement).
- If the scale factor is less than 1, the new triangle is smaller than the original triangle (a reduction).
- If the scale factor is equal to 1, the triangles are congruent (identical).
Example
Suppose we have two similar triangles, Triangle A and Triangle B.
- Triangle A has sides of length 3, 4, and 5.
- Triangle B has sides of length 6, 8, and 10.
To find the scale factor from Triangle A to Triangle B, we can use any corresponding pair of sides:
- Scale Factor = 6/3 = 2
- Scale Factor = 8/4 = 2
- Scale Factor = 10/5 = 2
In this case, the scale factor is 2, meaning Triangle B is twice as large as Triangle A.
Key Takeaway
The scale factor represents how much the sides of one triangle have been multiplied to obtain the corresponding sides of the similar triangle. It's a fundamental concept in understanding the relationship between similar figures.
