The focus so far has been on similar triangles, but there are also theorems that deal with similar
polygons
figures other than triangles. For example, the Angle-Angle Similarity (AA) theorem and the Side-Side-Side (SSS) similarity theorem are two theorems that deal with similar figures.
The AA similarity theorem states that if two angles of one figure are congruent to two angles of another figure, then the figures are similar. To prove that two figures are similar using the AA similarity theorem, you need to find two pairs of congruent angles in the figures.
Similarly, the SSS similarity theorem states that if the corresponding sides of two figures are proportional, then the figures are similar. To prove that two figures are similar using the SSS similarity theorem, you need to show that the ratios of the corresponding side lengths are equal.
To determine if two figures are similar using these theorems, you need to compare their corresponding angles or side lengths. If the angles or side lengths are congruent or proportional, respectively, then the figures are similar.
To apply the AA similarity theorem, you can start by identifying two pairs of congruent angles in the figures. Once you have identified the pairs of angles, you can conclude that the figures are similar.
To apply the SSS similarity theorem, you need to compare the corresponding side lengths of the figures. Determine the ratios of the corresponding side lengths and check if they are equal. If the ratios are equal, then the figures are similar.
Remember, proving that two figures are similar involves finding specific characteristics or properties that satisfy the conditions of the similarity theorems. By comparing angles and side lengths, you can determine if two figures are similar or not.