CRITERIOS de SEMEJANZA de Triángulos 📐

Understanding Triangle Similarity Criteria

Introduction to Triangle Similarity

• Susi introduces the topic of triangle similarity, explaining that certain criteria must be met for triangles to be considered similar.

First Criterion: Side-Side-Side (SSS)

• The first criterion is known as LLL (Side-Side-Side), which states that two triangles are similar if their corresponding sides are proportional.

• To verify this, one must establish the ratios of the corresponding sides. For example, comparing sides 6:2 and 12:4 should yield the same ratio.

• In this case, all ratios equal 3, confirming that the triangles are indeed similar because their sides maintain a consistent proportional relationship.

Second Criterion: Side-Angle-Side (SAS)

• The second criterion is LAL (Side-Angle-Side). It asserts that if two triangles have one angle in common and the sides forming that angle are proportional, then the triangles are similar.

• An example is provided where an angle is shared and side lengths of 8:4 and 6:3 yield a ratio of 2 for both pairs, indicating similarity without needing additional angles or side lengths.

Third Criterion: Angle-Angle (AA)

• The third criterion is A-A-A (Angle-Angle), which posits that if two triangles have all corresponding angles equal, they are similar.

• This criterion can also apply with only two angles known; knowing two angles allows for determining the third due to the triangle sum property (180 degrees).

Conclusion