Understanding Similar Triangles and Finding Corresponding Values | A Principle of Dividing Down and Scaling Back Up for Mathematics

If the sides given are larger, divide down by the greatest common factor. Do the computations in the smaller triangle and then scale back up.

This principle is based on the concept of similar triangles

This principle is based on the concept of similar triangles. Similar triangles are triangles that have the same shape but can have different sizes. The ratio of the corresponding sides of similar triangles remains constant.

If we have a larger triangle and want to find the corresponding values for a smaller triangle, we can use the principle of dividing down by the greatest common factor. The greatest common factor (GCF) is the largest number that can divide both larger side lengths evenly.

Let’s say we have a larger triangle with side lengths of 12 cm, 16 cm, and 20 cm. To find the corresponding values for a smaller triangle, we need to divide these side lengths by their greatest common factor. In this case, the GCF of 12, 16, and 20 is 4.

Dividing each side length by 4, we get a smaller triangle with side lengths of 3 cm, 4 cm, and 5 cm. These side lengths are in the same ratio as the original triangle but are scaled down.

Now, when performing computations in the smaller triangle, such as finding the area or perimeter, we do the calculations using the scaled-down side lengths. Once we obtain the result, we can scale it back up to find the corresponding values in the larger triangle.

For example, if we found that the area of the smaller triangle is 6 cm², we can scale it back up by multiplying it by the square of the scale factor. In this case, the scale factor is 4 (the GCF), so the area of the larger triangle would be 6 cm² * (4²) = 6 cm² * 16 = 96 cm².

This principle of dividing down and scaling back up allows us to work with similar triangles of different sizes and find corresponding values between them. It is a useful technique in geometry and mathematics.

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