How to Find Scale Factor
Verify that the figures are similar., Find a corresponding side length on each figure., Set up a ratio., Simplify the ratio.
Step-by-Step Guide
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Step 1: Verify that the figures are similar.
Similar figures, or shapes, are ones in which the angles are congruent, and the side lengths are in proportion.
Similar figures are the same shape, only one figure is bigger than the other.The problem should tell you that the shapes are similar, or it might show you that the angles are the same, and otherwise indicate that the side lengths are proportional, to scale, or that they correspond to each other. -
Step 2: Find a corresponding side length on each figure.
You may need to rotate or flip the figure so that the two shapes align and you can identify the corresponding side lengths.
You should be given the length of these two sides, or should be able to measure them.If you do not know at least one side length of each figure, you cannot find the scale factor.
For example, you might have a triangle with a base that is 15 cm long, and a similar triangle with a base that is 10 cm long. , For each pair of similar figures, there are two scale factors: one you use when scaling up, and one you use when scaling down.
If you are scaling up from a smaller figure to a larger one, use the ratio Scale Factor=largerlengthsmallerlength{\displaystyle {\text{Scale Factor}}={\frac {largerlength}{smallerlength}}}.
If you are scaling down from a larger figure to a smaller one, use the ratio Scale Factor=smallerlengthlargerlength{\displaystyle {\text{Scale Factor}}={\frac {smallerlength}{largerlength}}}.For example if you are scaling down from a triangle with a 15 cm base to one with a 10 cm base, you would use the ratio Scale Factor=smallerlengthlargerlength{\displaystyle {\text{Scale Factor}}={\frac {smallerlength}{largerlength}}}.Filling in the appropriate values, it becomes Scale Factor=1015{\displaystyle {\text{Scale Factor}}={\frac {10}{15}}}. , The simplified ratio, or fraction, will give you your scale factor.
If you are scaling down, your scale factor will be a proper fraction.If you are scaling up, it will be a whole number or improper fraction, which you can convert to a decimal.
For example, the ratio 1015{\displaystyle {\frac {10}{15}}} simplifies to 23{\displaystyle {\frac {2}{3}}}.
So the scale factor of two triangles, one with a base of 15 cm and one with a base of 10 cm, is 23{\displaystyle {\frac {2}{3}}}. -
Step 3: Set up a ratio.
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Step 4: Simplify the ratio.
Detailed Guide
Similar figures, or shapes, are ones in which the angles are congruent, and the side lengths are in proportion.
Similar figures are the same shape, only one figure is bigger than the other.The problem should tell you that the shapes are similar, or it might show you that the angles are the same, and otherwise indicate that the side lengths are proportional, to scale, or that they correspond to each other.
You may need to rotate or flip the figure so that the two shapes align and you can identify the corresponding side lengths.
You should be given the length of these two sides, or should be able to measure them.If you do not know at least one side length of each figure, you cannot find the scale factor.
For example, you might have a triangle with a base that is 15 cm long, and a similar triangle with a base that is 10 cm long. , For each pair of similar figures, there are two scale factors: one you use when scaling up, and one you use when scaling down.
If you are scaling up from a smaller figure to a larger one, use the ratio Scale Factor=largerlengthsmallerlength{\displaystyle {\text{Scale Factor}}={\frac {largerlength}{smallerlength}}}.
If you are scaling down from a larger figure to a smaller one, use the ratio Scale Factor=smallerlengthlargerlength{\displaystyle {\text{Scale Factor}}={\frac {smallerlength}{largerlength}}}.For example if you are scaling down from a triangle with a 15 cm base to one with a 10 cm base, you would use the ratio Scale Factor=smallerlengthlargerlength{\displaystyle {\text{Scale Factor}}={\frac {smallerlength}{largerlength}}}.Filling in the appropriate values, it becomes Scale Factor=1015{\displaystyle {\text{Scale Factor}}={\frac {10}{15}}}. , The simplified ratio, or fraction, will give you your scale factor.
If you are scaling down, your scale factor will be a proper fraction.If you are scaling up, it will be a whole number or improper fraction, which you can convert to a decimal.
For example, the ratio 1015{\displaystyle {\frac {10}{15}}} simplifies to 23{\displaystyle {\frac {2}{3}}}.
So the scale factor of two triangles, one with a base of 15 cm and one with a base of 10 cm, is 23{\displaystyle {\frac {2}{3}}}.
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Virginia Patel
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