What are similar triangles?
You’ve heard about similar triangles, but do you know what technically makes two triangles similar?
Informally, we can say that two triangles are similar if their associated angles are congruent. In other words, their angle measures have to be the same. However, the triangles don’t necessarily have to be the same size, in order for them to still be similar.
The formal definition of similar triangles tells us that two triangles are similar when the associated angles are congruent, and when the associated side lengths are proportional. If both of those conditions are present, then the triangles are similar. If either or both of those conditions are missing, then the triangles are not similar.
0:17 Informal definition of similar triangles // In order for two triangles to be similar, their angles have to the same, but the triangles themselves can still be different sizes.
0:32 Examples of similar triangles
0:45 Formal definition of similar triangles // In order for two triangles to be similar, their matching angles must be congruent, and the ratio of their matching sides are the same (their sides must be proportional).
2:02 Summary // If two triangles have the same angles and the same side lengths, then they’re congruent (they’re identical). If two triangles have the same angles but different side lengths, then they’re similar. It’s helpful to remember that, just like all squares are rectangles, all congruent triangles are similar triangles.