Comparing similar triangles
Two triangles are similar when the only difference is the scale, as shown in Figure 8.1, where Triangle (b) is a scaled-down version of Triangle (a):
Figure 8.1: Similar triangles
Two triangles are considered similar if they contain the same set of three corner angles. For example, if the angles (in degrees) of Triangle (a) are 60, 45, and 75, then the angles of Triangle (b) must also be 60, 45, and 75. The total of all angles in a triangle equates to 180 degrees.
For similar triangles, the following applies:
- All corresponding angles are equal
- All corresponding sides have the same ratio
- Corresponding sides have the same ratio between them
As triangles are only considered similar if the respective angles are the same between them, as previously discussed. Given Figure 8.1, A = α, B = β, and Γ = γ.
Because, with similar triangles, one is smaller than the other, the ratio of the corresponding...
