![Picture](/uploads/2/0/1/1/20114429/5208750.jpg?471)
Similar figures are shapes who share a ratio of side lengths, like the figure to the left. The side lengths may be different, but when you simplify the ratio:
10/20 = 1/2
5/10 = 1/2
Both figures have a height to base ratio of 1 to 2 or 1/2.
Some rules for similar figures;
1. Must be the same shape.
2. Must have the same interior angle measurements.
3. Must have the same ratio of side lengths (shown above).
4. Side lengths do not have to be the same.
You can use ratios of similar figures to find a missing side length:
10/20 = 1/2
5/10 = 1/2
Both figures have a height to base ratio of 1 to 2 or 1/2.
Some rules for similar figures;
1. Must be the same shape.
2. Must have the same interior angle measurements.
3. Must have the same ratio of side lengths (shown above).
4. Side lengths do not have to be the same.
You can use ratios of similar figures to find a missing side length:
The ratio of height to base on the smaller triangle is 2 to 3. We can use that ratio in a proportion to find the height of the larger triangle. We have to multiply the base of the smaller triangle by 2 to get the larger base, so we must multiply the height of the smaller triangle by 2 as well.
The height of the smaller triangle multiplied by 2 is 4, so the height of the larger triangle is 4. |
The amount by which a figure is increased in size is called the scale factor. In our triangle example above, the scale factor was 2 because the height and the base were each 2 times as long in the larger triangle. Scale factors can be fractions or whole numbers, but they must be applied to all measurements, not just one:
This would not be an example of similar figures, because the ratios are not the same. The scale factor has only been applied to the height of the figure.
This is another example of scale factor only being applied to one measurement, in this case the base length. These figures are also not similar In this example, the scale factor has been applied to both the base length and the height, meaning that the ratio of side lengths has remained the same. In this case, our scale factor is 4, since: The height of 3 increase by a factor of 4 to equal 12. The base length of 5 increased by a factor of 4 to equal 20. |