Similar Figures
Similar figures in Grade 7 geometry have the same shape but may differ in size — corresponding angles are equal and corresponding sides are proportional. In Saxon Math, Course 2, students identify similar figures and use proportions to find missing side lengths. For example, a triangle with sides 3, 4, 5 is similar to one with sides 6, 8, 10 (scale factor 2). Understanding similarity is the foundation for map reading, scale models, photography, and trigonometry in high school math and science.
Key Concepts
Property Two figures are similar if they have the same shape even though they may vary in size.
Examples A triangle with sides 3, 4, 5 is similar to one with sides 6, 8, 10 because each side is doubled. All squares are similar because they all have four $90^{\circ}$ angles and proportional sides. A tall, skinny rectangle is not similar to a short, wide rectangle because their side ratios differ.
Explanation Imagine you have a favorite photo and you use a photocopier to shrink or enlarge it. The new photo is a different size, but everyone in it has the same proportions—that's similarity! Similar figures have matching angles, but their side lengths are scaled up or down by the same factor. They are proportional copies of each other.
Common Questions
What are similar figures in Grade 7 math?
Similar figures have the same shape with equal corresponding angles and proportional corresponding sides. They may be different sizes but are otherwise identical in form.
How do you prove two figures are similar?
Show that all corresponding angles are equal AND all corresponding sides are in the same ratio (same scale factor).
How do you find a missing side length in similar figures?
Set up a proportion using corresponding sides: (side of figure 1) / (side of figure 2) = (known side of figure 1) / (known side of figure 2). Solve by cross-multiplying.
Are all squares similar to each other?
Yes, all squares are similar because they all have four 90° angles and sides in proportion. The scale factor between any two squares is the ratio of their side lengths.
Where are similar figures taught in Saxon Math Course 2?
Similar figures are covered in Saxon Math, Course 2, as part of Grade 7 geometry and proportional reasoning content.
What is the difference between similar and congruent figures?
Congruent figures have the same shape AND the same size (scale factor = 1). Similar figures have the same shape but may differ in size.
How do similar figures appear in real life?
Scale models, maps, blueprints, enlarged or reduced photographs, and architectural drawings all use the principle of similar figures.