๐ What are Similar Polygons?
Similar polygons are polygons that have the same shape but can be different sizes. This means their corresponding angles are congruent (equal), and their corresponding sides are proportional.
- โ๏ธ Corresponding angles are equal.
- ๐ Corresponding sides are in proportion.
- ๐ Think of it like a scaled version of the original.
๐ What are Congruent Polygons?
Congruent polygons are polygons that have the same shape and the same size. This means all corresponding angles and all corresponding sides are congruent (equal).
- ๐งฉ All corresponding angles are equal.
- ๐ All corresponding sides are equal.
- ๐ฏ Think of it like an exact copy.
๐ Similar vs. Congruent Polygons: The Key Differences
| Feature |
Similar Polygons |
Congruent Polygons |
| Shape |
Same |
Same |
| Size |
Different (proportional) |
Same |
| Corresponding Angles |
Congruent (equal) |
Congruent (equal) |
| Corresponding Sides |
Proportional |
Congruent (equal) |
| Ratio of Sides |
Constant scale factor ($k$) |
Scale factor of 1 |
| Example |
Two squares, one with side length 2 and the other with side length 4 |
Two squares, both with side length 3 |
๐ก Key Takeaways
- ๐ Similarity involves proportional sides and congruent angles; think of scaled versions.
- ๐ฏ Congruence demands both the same shape and the same size; think of exact copies.
- ๐ All congruent polygons are similar, but not all similar polygons are congruent. Congruence is a special case of similarity where the scale factor is 1.