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.

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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.

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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.