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I can apply three commonly used theorems to establish proportionality. The three commonly used theorems would be the side splitter theorem, if 3 or more parallel lines are intersected by 2 transversals theorem, and the theorem that talks about a ray bisects an angle of a triangle. Each of these theorems was a little confusing for me to comprehend, but looking back at these notes and seeing the visuals and examples for each one made it easier to understand. I am always looking back at these notes, and still sometimes struggle remembering the differences between each one, but if I didn't have these notes, I would be extremely lost.

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I can solve shadow problems. I understand shadow problems very well and visualizing them is easy for me to do. Sometimes I have to draw a picture to really understand it though. Using this example, I was able to base all other shadow problems off of this and be successful in solving them correctly.

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I can use the concept of similarity to establish the congruence of angles and the proportionality of sides. Basically what this is saying, is that so now that you have similar figures, what else can you prove? The answer to that is corresponding angles are congruent and corresponding sides are proportional to each other. This concept was easy to learn because it is the same all the time. If you ever have a similar figure, both these things will be true.

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I can use several methods to prove that triangles are similar. There are 4 methods that are used to prove triangles similar. You could use angle angle angle similarity, angle angle similarity, side side side similarity, or side angle side similarity. These notes clearly display this because it shows what each one is proving and it also gives examples of what the diagrams will look like. I came back to this sheet many times on homework trying to remember how to do it, and it finally clicked and now I understand it.

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I can identify the characteristics of similar polygons. This example from notes makes this a simple and easy thing to learn and know. All that makes shapes similar is that they are the same shape, but different sizes. This put that whole concept in easy terms for me to understand and actually made learning about similarity easier because I knew exactly what it was.

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I can calculate geometric means. Calculating geometric means is easy. All you have to do is use the two numbers that you get from the problem and put them diagonal of each other. Then, you fill in x's where there are no numbers. Cross multiply and then solve for x and you will end up with the geometric mean. This example from notes helps me understand that because it gives an example and also just displays what the problem will look like while executing it.

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I can apply the product ratio theorem. This is also known as the means-extremes ratio theorem. I had a little bit of a hard time understanding this concept at first, but now I know that basically what it is, is that the diagonal quantities are equal.

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I can recognize and work with proportions. This example from notes about proportions is also very clear. It gives the definition and some examples. I can clearly see that a proportion is just like a bunch of equal fractions. I understand this concept very well and think that this example helped me understand it so well.

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I can recognize and work with ratios. This definition from notes helps me understand this concept because it makes it very clear what a ratio is and it also has examples, so I know what to compare everything to if I see a ratio in my homework.