Two geometric figures are said to be similar if they have the same shape regardless of the size differences between them. For triangles, we have the following criteria that help us determine when they are similar:
Angle-Angle Criterion (AA)
Two triangles are similar if they have two equal angles.
Side-Side-Side Criterion (SSS)
Two triangles are similar if they have proportional sides.
Side-Angle-Side Criterion (SAS)
Two triangles are similar if they have two proportional sides and the angle between them is equal.
Similarity of Triangles
Similarity Criteria for Right Triangles
Two right triangles are similar if they have one equal acute angle.
Two right triangles are similar if they have the two legs proportional.
Two right triangles are similar if the hypotenuse and one leg are proportional.
Exercises on Triangle Similarity
Determine whether the following triangles are similar:
1
Solution:
They are similar because they have their 3 sides proportional.
2
Solution:
They are similar because they have two equal angles.
3
Solution:
and 
and
They are similar because they have two proportional sides and one equal angle.
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