First similarity criterion

To establish whether two triangles are similar, there is no need to check all the conditions of the definition: it is enough to compare the angles.

Theorem — First similarity criterion

If two triangles have two angles respectively congruent, then they are similar.

The criterion works because the sum of the interior angles of a triangle is always $180°$: if two angles coincide, the third automatically coincides as well, and so the two triangles have the same shape.

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Topics: Similarity
Concepts: Similarity criteria · Similar triangles
Methods: Similarity criteria
Skills: Synthetic geometry