Similarity is an important concept in geometry that helps prove some theorems and their corollaries. The statement of similarity is based on the fact that for two shapes to be similar, they have to have the same angles and their sides have to be in proportion. A similarity statement has to clearly explain why two shapes are similar. It is used to prove a theorem. It can also be used to find the value of a side of a shape.
To write a similarity statement, start by identifying and drawing the similar shapes. See where the equal angles are and draw the shapes accordingly. Label all the angles. Write down all the congruent angles (for example, angle ABC is congruent to angle DEF, angle BCA is congruent to angle EFD, etc.).Then, calculate all the lengths of the sides of the triangles and confirm that they are in proportion.
After that, you are ready to write the similarity statement. You will write "Triangle ABC ~ Triangle DEF." This symbol, ~, indicates congruency. Remember that congruent shapes have the same size AND shape, while similar shapes have the same shape but not necessarily the same size. The sides of similar shapes are always in proportion.