Enlargements and Reductions
2 different shapes, one is the original and one is the model/image. The model/image is the enlarged/reduced shape. The shapes are enlarged or reduced by the scale factor, which can be found easily as it is the number you either multiplied or divided the original by to find the model.
Scale Factor/Ratio
For example, on a map, it would have a ratio of 1m:3km. The first number would most likely be the original, and you can find what the measurements would be if you had the actual measurement as x:21km. It can help to make the ratios into fractions, and to use the Butterfly method to find out what x is. In this example, x would be equal to 7m to make it equal 21km.
Butterfly Method
As explained above quickly, you can put the numbers in fraction form beside each other and efficiently multiply them to solve any unknown variables. After multiplying 4 and 9 together, as well as 7 and y, you end up with 36=7y. You then divide by 7 in order to find what 1x is. At the end step, if the number does not divide evenly, you can leave it in fraction form.
Triangles
How can you tell what the scale factor is? You can match up the sides, and put them into a fraction, with the image on top and the original on the bottom. First, I named each of the angles, and used a formula that helps me show my work easier. After making the fractions, you have to solve to find the missing variables. I use the Butterfly method to multiply because it is easier for me to understand. Then you divide each fraction by what x or y is and find the ultimate answer. I rewrote the triangles with the complete filled in variables, and then I divided the numbers of the variables by the original numbers. I found that the numbers were each given an answer of 6 for all 3, which means that the scale factor is 6.
Types of Angles
Acute-Less than 90 degrees
Right-90 degrees
Obtuse-90-180 degrees
Straight-A straight line/angle, 180 degrees
Reflex-More than 180 degrees
Supplementary-Have nice, friendly numbers, easy to do
Complementary-Angles that go with corners
Triangles-All 3 sides add up to 180 degrees
