Two similar polygons are two figures with the same number of sides and angles, but different sizes. To be considered similar, their corresponding angles must be equal and their corresponding sides must be in proportion. This means that if two sides are multiplied by the same number, the resulting lengths of those sides will be proportional. Additionally, the ratio between the two polygons must be constant, meaning that all of the sides of one polygon will have the same ratio when compared to the other.
7 Examples of Two Similar Polygons
1. Triangles: A triangle is a three-sided polygon and they can be similar when their corresponding angles are equal and their corresponding sides are in proportion. For example, a triangle with sides of 4, 5, and 6 will have a ratio of 4:5:6. A similar triangle with sides of 8, 10 and 12 will have the same ratio of 8:10:12.
2. Quadrilaterals: A quadrilateral is a four-sided polygon and they can be similar when their corresponding angles are equal and their corresponding sides are in proportion. For example, a quadrilateral with sides of 4, 7, 8 and 9 will have a ratio of 4:7:8:9. A similar quadrilateral with sides of 8, 14, 16 and 18 will have the same ratio of 8:14:16:18.
3. Pentagon: A pentagon is a five-sided polygon and they can be similar when their corresponding angles are equal and their corresponding sides are in proportion. For example, a pentagon with sides of 3, 5, 6, 7 and 8 will have a ratio of 3:5:6:7:8. A similar pentagon with sides of 6, 10, 12, 14 and 16 will have the same ratio of 6:10:12:14:16.
4. Hexagon: A hexagon is a six-sided polygon and they can be similar when their corresponding angles are equal and their corresponding sides are in proportion. For example, a hexagon with sides of 3, 5, 7, 9, 10 and 11 will have a ratio of 3:5:7:9:10:11. A similar hexagon with sides of 6, 10, 14, 18, 20 and 22 will have the same ratio of 6:10:14:18:20:22.
5. Heptagon: A heptagon is a seven-sided polygon and they can be similar when their corresponding angles are equal and their corresponding sides are in proportion. For example, a heptagon with sides of 4, 6, 8, 10, 12, 14 and 16 will have a ratio of 4:6:8:10:12:14:16. A similar heptagon with sides of 8, 12, 16, 20, 24, 28 and 32 will have the same ratio of 8:12:16:20:24:28:32.
6. Octagon: An octagon is an eight-sided polygon and they can be similar when their corresponding angles are equal and their corresponding sides are in proportion. For example, an octagon with sides of 4, 6, 8, 10, 12, 14, 16 and 18 will have a ratio of 4:6:8:10:12:14:16:18. A similar octagon with sides of 8, 12, 16, 20, 24, 28, 32 and 36 will have the same ratio of 8:12:16:20:24:28:32:36.
7. Nonagon: A nonagon is a nine-sided polygon and they can be similar when their corresponding angles are equal and their corresponding sides are in proportion. For example, a nonagon with sides of 3, 5, 6, 7, 8, 9, 10, 11 and 12 will have a ratio of 3:5:6:7:8:9:10:11:12. A similar nonagon with sides of 6, 10, 12, 14, 16, 18, 20, 22 and 24 will have the same ratio of 6:10:12:14:16:18:20:22:24.
Similar polygons are two polygons with the same number of sides and angles, but different sizes. To be considered similar, their corresponding angles must be equal and their corresponding sides must be in proportion. There are seven examples of two similar polygons, including triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, and nonagons. Understanding the concept of similar polygons can help you solve complex problems in geometry.
