# 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.