Similarity ratios

Learning Objectives Define the ratio of similarity (scale factor) between two similar figures. Set up and solve proportions to find unknown side lengths of similar polygons. Relate the ratio of similarity to the ratio of perimeters of similar figures. Calculate the ratio of areas of similar figures using the square of the ratio of similarity. Calculate the ratio of volumes of similar 3D figures using the cube of the ratio of similarity. Apply similarity ratios to solve multi-step geometric and real-world problems. How can an architect build a detailed, tiny model of a massive skyscraper and know it's perfectly proportioned? 🏙️ It's all about the power of similarity ratios! This tutorial explores the core concept of similarity ratios, also known as the scale factor...

TermDefinitionExample Similar PolygonsTwo polygons are similar if their corresponding angles are congruent and the lengths of their corresponding sides are in proportion.Triangle ABC with sides 3, 4, 5 is similar to Triangle XYZ with sides 6, 8, 10 because all corresponding sides have a ratio of 1:2 (e.g., 3/6 = 4/8 = 5/10 = 1/2). Ratio of Similarity (Scale Factor)The constant ratio between the lengths of corresponding sides of two similar figures. It is often denoted by the variable 'k'.If side AB of a small triangle is 5 cm and the corresponding side XY of a larger, similar triangle is 15 cm, the ratio of similarity from the small triangle to the large one is 5/15 = 1/3. Corresponding SidesSides that are in the same relative position in two similar figures. They are the sides...

Ratio of Perimeters If the ratio of similarity (side lengths) of two figures is a:b, then the ratio of their perimeters is also a:b. Use this rule to find a missing perimeter when you know the scale factor and the other figure's perimeter. It's a direct 1-to-1 relationship. Ratio of Areas If the ratio of similarity of two figures is a:b, then the ratio of their areas is a²:b². Use this rule to find a missing area. Remember to square the side length ratio before setting up your proportion for the areas. Ratio of Volumes If the ratio of similarity of two 3D figures is a:b, then the ratio of their volumes is a³:b³. Use this for 3D figures like prisms, pyramids, cylinders, and spheres. You must cube the side length ratio to find the volume ratio.