In this unit, I learned about right angles, degrees, enlargements and reductions, and I also learned how to find the actual length of an object, scale factors and missing side lengths. A scale factor is the ratio of any corresponding length in two similar shapes like triangles. And a scale factor is equivalent to a scale or known as a ratio.
What are enlargements and reductions?
An enlargement is when the original proportion was increased or got larger. While a reduction is when the original proportion was decreased or got smaller. If the scale factor is more than one, it’s an enlargement, and if the scale factor is less than one it’s considered as a reduction.
Here’s an example of two similar triangles:
This is my example of an enlargement and my original is the one on the left and my model or image is on the right, but you can actually decide which would be your image and actual. Since we know all the side lengths on both sides of these triangles, we also want to know it’s scale factor and if they are similar, here’s how:
First is to find which side lengths correspond to each other. Then make it into ratios, and it is important to know that the image goes on top of the original (image/actual).
Next is to divide each of the fractions by itself and if all of the results are the same, they are similar and, that number is the scale factor.
If there are missing side lengths, we must make an equation, use the distributive property, and use the butterfly method or the cross-multiply way:
As you can see, there are two missing side lengths. So, what we should do is to find their corresponding side length, and make them all into a ratio. Don’t forget where your model and original goes when putting them all into a ratio.
And we also need to find the scale factor – which we must find a ratio that has the side lengths already. You can leave the fraction by itself or you can divide it if possible:
Then we are now making an equation, and since there are two fractions we will distribute the scale factor to each of them. Then solve the equation by using the butterfly method:
I’ve also learned about overlapping triangles, which is a bit complex because there are two triangles that are placed on top of another triangle, and I have to find the missing side lengths, find the scale factor, expanding the triangles by separating them, and solving equations.
There are two missing side lengths.
Add the (4 and x) together and also (6 + 5). Then expand into two separate triangles.
Distribute the scale factor to the two fractions.