Notes
similarity
Similarity
Two shapes are similar if one can be obtained from the other by a series of rotations, reflections, translations, and scaling.
If two shapes are similar then the following hold:
- Corresponding angles on the two shapes are equal.
- There is a fixed scale factor such that corresponding lengths on the two shapes are related by multiplying by this scale factor.
- The ratio of two lengths in one shape is the same as the ratio of the corresponding lengths in the other.
Similar Triangles
When the two shapes are triangles then the following statements are equivalent:
- The two triangles are similar
- The angles in one triangle are the same as the angles in the other
- The ratios of the lengths in one triangle are the same as in the other
Created on June 23, 2021 20:09:04
by
Andrew Stacey