Mary is mistaken in her conclusion that the two triangles are not similar because size does not determine similarity. Similarity is determined by the proportionality of corresponding sides and the congruence of corresponding angles. Congruence is the equality of all the measures of the corresponding parts of two figures.
In order to determine if two triangles are similar, we must compare the ratios of corresponding sides. If the ratios of corresponding sides are equal, then the triangles are similar. In the diagram, it is not specified what the measures of the sides of the triangles are, so it is not possible to determine if the triangles are similar based on the information given. However, if the ratio of corresponding sides are same, then the triangles are similar.
It is important to note that similarity and congruence are different concepts. Congruence refers to the equality of all measures of corresponding parts of two figures, including side lengths and angles. Similarity refers to the proportionality of corresponding parts, including side lengths and angles. A triangle can be similar to another triangle without being congruent, and congruent triangles are always similar.
In summary, Mary is mistaken because the size of the triangle does not determine similarity, it is determined by the proportionality of corresponding sides and congruence of corresponding angles. Without knowing the measures of the sides of the triangles, it is impossible to determine if the triangles are similar based on the information given.