Two triangles are considered similar if they have the same shape but not necessarily the same size. There are three main conditions that can determine if two triangles are similar:
- Side-Side-Side (SSS) Similarity: If the corresponding sides of two triangles are proportional, then the triangles are similar.
- Side-Angle-Side (SAS) Similarity: If two pairs of corresponding sides are proportional and the included angles are congruent, then the triangles are similar.
- Angle-Angle-Angle (AAA) Similarity: If two corresponding angles of two triangles are congruent, then the triangles are similar.
Visual Representation:
Example:
If Triangle ABC has sides AB = 3, BC = 4, and CA = 5, and Triangle DEF has sides DE = 6, EF = 8, and FD = 10, then Triangle ABC is similar to Triangle DEF because their corresponding sides are proportional (3/6 = 4/8 = 5/10). This is an example of SSS similarity.
In essence, two triangles are similar if their corresponding sides are proportional or their corresponding angles are congruent.
