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Calculate the scale factor and ratios between corresponding sides of similar triangles
1:1
6 : 4
1:1
9 : 6
1:1
12 : 8
When two triangles are similar, their corresponding sides are proportional. The ratio between any pair of corresponding sides is called the scale factor. This scale factor is constant for all three pairs of corresponding sides.
The scale factor is the multiplier that relates corresponding sides. If the scale factor is 2, the second triangle is twice as large as the first.
Ratios are written as a:b and represent the relationship between corresponding sides. A ratio of 3:2 means the first side is 1.5 times the second.
Corresponding sides are matched by size: smallest to smallest, largest to largest. Proper identification is crucial for accurate calculations.
If triangles are similar, the ratio a'/a = b'/b = c'/c, where primed letters represent the larger triangle's sides.
Divide any side of the larger triangle by the corresponding side of the smaller triangle. For example, if corresponding sides are 12 and 4, the scale factor is 12 ÷ 4 = 3.
If the ratios between corresponding sides aren't equal, the triangles are not similar. Check that you've correctly identified corresponding sides (smallest to smallest, etc.).
Yes! If Triangle 2 is smaller than Triangle 1, the scale factor will be less than 1. A scale factor of 0.5 means Triangle 2 is half the size of Triangle 1.
Sort the sides of both triangles from smallest to largest. The smallest side of one triangle corresponds to the smallest side of the other, and so on.
They're essentially the same concept expressed differently. The scale factor is the decimal form (like 1.5), while the ratio is the fractional form (like 3:2 or 3/2).
Yes! If you know two sides are similar and you know three of the four measurements, you can set up a proportion to find the fourth. For example: 4/6 = x/9, so x = 6.
No! If the scale factor for sides is k, the scale factor for areas is k². A triangle with sides twice as long has an area 4 times as large.
In real-world measurements, small differences due to rounding are normal. Ratios within 1-2% of each other usually indicate similar triangles, accounting for measurement error.
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