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.

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.

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.

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.