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.