Figures are Mathematically similar when the corresponding angles are all congruent and they share a scale factor.

These two rectangles are SIMILAR

We are going to call the rectangle with the dimensions 6 and 12 rectangle a and we are going to call the other one rectangle b. These 2 figures are similar for a couple reasons. One of the biggest reasons is because they share a scale factor. From rectangle b to rectangle a the scale factor is 3. A scale factor is ONE number. A scale factor is the difference between two rectangles that are similar. For example with these rectangles, if 2×3=6 then you HAVE TO multiply 4 by 3 because a scale factor is one number.

Another reason that they are similar is because the all of the corresponding angles are congruent. This means that the matching angles are all the same; they have the same angle measurement. In this case all of the similar angles are all 90 degrees.

 These two triangles are SIMILAR

Triangles just like rectangles can be similar due to the fact that they have a s.f (scale factor) in common. The smaller triangle we will call triangle A and we will call the other triangle B. From triangle A to triangle B the s.f will be 2 and from B to A will be 1/2 or the reciprocal of 2. Another reason that these triangles are similar is because they are the same basic shape. They are both triangles. If you have a rectangle and a triangle there is no possible way that they could similar to each other due to a couple reasons one of them being that they aren’t the same general shape. All the triangles corresponding angles are also congruent.