Similar and Congruent Polygons
Grade 8 math lesson on similar and congruent polygons, including scale factors and proportional relationships. Students learn to distinguish similar polygons (same shape, different size) from congruent polygons (same shape and size) and use proportions to find missing measurements.
Key Concepts
New Concept This course bridges arithmetic with algebra and geometry. We will use familiar math skills to describe the world around us in new ways. What’s next To begin, we will define similarity and congruence. Then, we'll apply these rules with worked examples to find unknown lengths and explore scale factors.
Common Questions
What is the difference between similar and congruent polygons?
Congruent polygons are identical in both shape and size — corresponding sides are equal in length and corresponding angles are equal. Similar polygons have the same shape but different sizes — corresponding angles are equal and corresponding sides are proportional.
What is a scale factor between similar polygons?
The scale factor is the ratio of corresponding side lengths in two similar polygons. If the scale factor is 2, every side of the larger polygon is twice the length of the corresponding side in the smaller polygon.
How do you find a missing side length in similar figures?
Set up a proportion using the known corresponding sides to find the scale factor, then apply it to find the missing side. For example, if triangles have corresponding sides 3 and 6, the scale factor is 2, so a side of 5 corresponds to a side of 10.
How do you prove two polygons are similar?
Two polygons are similar if all corresponding angles are equal AND all corresponding sides are proportional (same ratio). Both conditions must be satisfied for similarity.