Proportions

Learning Objectives Identify the scale factor between two similar polygons. Set up and solve proportions to find the unknown perimeter of a similar figure. Set up and solve proportions to find the unknown area of a similar figure. Articulate the relationship between the scale factor, the ratio of perimeters, and the ratio of areas. Determine the scale factor given the ratio of the areas of two similar figures. Solve multi-step problems involving proportions, area, and perimeter in real-world contexts. Ever wonder how architects create a tiny blueprint that becomes a massive skyscraper? 🏙️ It's all about scaling and proportions! In this tutorial, we will review how to use proportions to solve problems involving the perimeter and area of similar geometric figures. Unders...

TermDefinitionExample RatioA comparison of two quantities by division. It can be expressed as a fraction (a/b), with a colon (a:b), or with the word 'to' (a to b).The ratio of 3 boys to 5 girls in a class is 3/5 or 3:5. ProportionAn equation that states that two ratios are equal.1/2 = 4/8 is a proportion because both ratios are equivalent. Similar FiguresTwo geometric figures that have the same shape but are not necessarily the same size. Their corresponding angles are congruent, and the ratios of their corresponding side lengths are equal.A 3x4 rectangle and a 6x8 rectangle are similar because their corresponding angles are all 90° and the ratio of corresponding sides is 3/6 = 4/8 = 1/2. Scale Factor (k)The constant ratio of any two corresponding side lengths of two similar fig...

Ratio of Perimeters of Similar Figures If the scale factor of two similar figures is a/b, then the ratio of their perimeters is also a/b. P_1 / P_2 = a / b Use this rule when you know the scale factor (or can find it from side lengths) and need to find a missing perimeter. The relationship is linear. Ratio of Areas of Similar Figures If the scale factor of two similar figures is a/b, then the ratio of their areas is (a/b)². A_1 / A_2 = (a / b)^2 = a^2 / b^2 Use this rule when dealing with the area of similar figures. Remember to square the scale factor because area is a two-dimensional measurement.