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Figures are mathematically similar when…
There are very few requirements shapes have to meet for them to be similar. The first is all corresponding angles must be congruent. If they are not, the shapes are not similar. Second, the corresponding sides of both shapes must have a scale factor from one shape to the second. If we are doing problems like we did earlier in the year with Wumps, the new coordinates must have the same coefficient. Finally, they must have the same general shape. A triangle cannot be similar to a trapezoid because they do not have the same general shape. But, for triangles they only need to have corresponding angles be congruent for the two triangles to be similar. Scale factors do not matter with triangles.
Any Two Rectangles are Similar
False
To see if any two rectangles are similar, lets see if they meet the rules
Are the general shapes the same?
Yes. They two rectangles are both rectangles.
Are the corresponding angles congruent?
Yes. For a shape to be considered a rectangle, all angles must be 90 degrees. So all angles are congruent between the two shapes.
Is there a scale factor?
No. Not all rectangles have scale factors. If you take one pair of corresponding sides and find the scale factor, the scale factor isn’t always the same for the other pair of corresponding sides. This makes them not similar. Below is an example of two rectangles (u and t) that are not similar on a worksheet we did in class.
Below is the blog post where I explained it.
Any two equilateral triangles are similar
True
To see if any two equilateral triangles are similar, lets see if they meet the rules.
Are the general shapes the same?
Yes. They two triangles are both equilateral triangles.
Are the corresponding angles congruent?
Yes. For a shape to be considered a equilateral triangles, all angles must be 60 degrees. So all angles are congruent between the two shapes.
Is there a scale factor?
Yes. Because all side lengths are the same, they would all change the same way to become another equilateral triangle.
When I started this assignment I was a little scared because there were so many shapes. I then realized that they can each fit into three categories of general shapes, and then I only have to worry about the shapes in those categories and if they are similar or not. One category was just shape v, and so there was nothing for that to be similar to so I knew v wasn’t similar to anything. Then I went to the triangles. I measured the side lengths, and then realized x can’t be similar to y or w because the not all the corresponding angles were congruent. Then, I realized y and w are similar because all the corresponding angles were congruent, and there was a scale factor from y to w of 2. I then went on to the rectangles. I immediately knew u could not be similar to anything because there was no scale factor to any of the other triangles. I then saw t and z were similar because the corresponding side lengths from t to z, the lengths had doubled. That meant the scale factor from t to z was 2. 
For the next side I started by measuring the sides of the original shape. The original rectangle (E) had a length of 4 and the other one was 3. I then created another triangle that was the same as E, just had lengths of 2 and 1.5 (A), and so the scale factor from E to A was 1/2. For next question, I just created a rectangle that had no scale factor to E. For the next question, I created another triangle that had the same angles as the original (F), just the side lengths were 1/2 the size. For the last question, I made a right triangle because then the corresponding angles weren’t congruent so it wasn’t similar.
Tilda Sutter Math Profile
B 9.12.16
Math is something that I think I am overall pretty good at. I think it came as something that was easy to me in 2nd Grade (but that may be because I have trouble remembering before that). But overall I think my best year at math was 5th Grade. In fifth grade we did a lot of problems where we would need to find patterns and create patterns. I think it got a little harder for me in 6th Grade. I have trouble multiplying and dividing quickly, and during timed tests when I try to go fast my numbers come out incorrect. I like learning math. I like learning problems where we can’t just plug in the numbers, that look really confusing at the start and then when you’re done it just kind of feels satisfying. Like a problem where using a calculator won’t give you that much of an advantage. But there are some things I don’t like about learning math. I don’t like when we start a new unit and you have to learn a lot of different stuff at once. It gets really overwhelming. But overall I think I am a good math student. I try really hard to be one at least. When I’m home and studying, I try to break the assignment into parts and do them on different days if it’s a long assignment. If it’s short, I try to do it in one day. That is the kind of math student I am.
#28
18=______% of 150
18=______% x 150?
How Do We Solve This?
18=______% x 150? is the same as 18/150=_____%!
18/150=12%
Here is a Story Problem:
Stella was waiting in another really long line for pencils. The cashier came back and said, “A pack of pencils is 150 pencils. I’ll give you 18 while your waiting in line.” What is the percent of the pack of pencils Stella was given in line?
#27
8 1/2 of 500.00$ =______?
8.5 x 500 =____?
How Do We Solve This?
We do multiplication! 8.5 x 500
8.5 x 500 = 42.5!
Here is a Story Problem:
Stella was was waiting in another really long line to get a pack of pencils. The pack of pencils was 500.00$. She was told she could skip the line if she paid an extra 8 1/2% of the pack of pencils. How much did Stella pay to skip the line?
#26
40=20% of what number?
40=20%x______?
How Do We Solve This?
40=20%x____? is the same as 40/.20!
40/.20=200!
Here is a Story Problem:
Stella was waiting in line for a pack of pencils. The line was very long. A cashier came to the people waiting in line and said, “I’ll give you now in line 20% of the pencils you will get at the end of the line.” Stella was given 40 pencils. How many pencils is a whole pack of them?
Lately, we have been having pop quizzes before class. At first I wasn’t doing so well, as shown in the first picture. I started having little panics, going home and doing a lot of studying. I started getting better and soon I was getting steady threes, but then recently, I got a four. I am really proud of my progress and hope I continue to grow.
The take home test is a strength of mine. I studied really hard by practicing my fractions at home. I would practice every night leading up to the test. When the test came I would do it every night and then check my answers around a million times. I am really proud of my score and I feel that I earned it.
Xtramath is a struggle for me. It is one thing that I have trouble with. It is hard for me to type the answers in that quickly. I also find that when I study the problems out of xtramath I get them right in under three seconds but when I do xtramath I just forget all of them. Another problem I have is I forget to do it a lot. That is why it is a struggle for me that I am working on improving.
My notebook always has been really neat. It is a strength of mine. I try to keep it neat so I can look back at my work and understand and feel comfortable sharing it. At the beginning of last year I had a really messy notebook and I tried to improve. I worked really hard and now all my work is neat.