# Similarity

# Understanding Similarity

*Similarity*in geometry refers to the relationship between shapes that have the same shape but different sizes.- Two shapes are
**similar**if their corresponding angles have the same measure and their corresponding sides are in proportion. - Similarity applies to all types of shapes, including triangles, circles, rectangles, and complex shapes.

# Fundamentals of Similar Triangles

**Similar triangles**have the same shape but may differ in size.- Understand the properties of similar triangles: their corresponding angles are equal, and corresponding side lengths are in proportion.
- Familiarize yourself with the concept of
**ratio of similarity**, which is the ratio of the lengths of corresponding sides in similar triangles.

# Discovering Similar Triangles

- If two angles in one triangle are congruent to two angles of another triangle, then these triangles are similar (the
*AA*similarity criterion). **The SAS**similarity criterion states that if two sides in a triangle are proportional to two sides of another triangle, and the included angles are congruent, then these triangles are similar.**The SSS**similarity criterion states that if three sides in a triangle are proportional to three sides of another triangle, then these triangles are similar.

# Working with Similar Shapes

- With similar figures, you can create
**scale factors**to determine unknown side lengths or other dimensions. - Use
**proportions**to solve problems involving similar figures. If two figures are similar, then the ratios of the lengths of their corresponding sides are equal.

# Applying Similarity Concepts

- Emphasize the importance of similar figures in real-world applications, such as in building scale models, maps, and blueprints.
- Understand that many problems involving angles, lengths, and distances can be solved using the properties of similar figures.