More Information About Similar Figures
In mathematics, polygons are similar if their corresponding angles are congruent and the ratio of their corresponding sides are in proportion.
Once we know that triangles (or any polygons) are similar, we also know some additional facts about the figures.
- Ratio of Perimeters, Altitudes, Medians, Diagonals, and Angle Bisectors
If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio.
Example:
If the sides of two similar triangles are in the ratio 4:9, what is the ratio of their perimeters?
Answer: 4:9 - Ratio of Areas
If two polygons are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Example:
If the sides of two similar triangles are in the ratio of 3:5, find the ratio of their areas.
Answer: 9:25 - Ratio of Volumes
If two polygons are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides.
Example:
If the sides of two similar triangles are in the ratio of 2:3, find the ratio of their volumes.
Answer: 8:27