Lesson 1: The Tangent Ratio - Similarity, Angles and Ratios

   Constructing Knowledge


One conclusion you may have drawn from the previous investigation is that if two right triangles contain one pair of identical acute angles, the other pair of acute angles must also be identical. Both triangles will then have the same three angle measures and will be similar. In summary, if two right triangles contain one pair of identical acute angles, the two triangles are similar.


So far, you have looked at two important relationships:

  • The ratio of corresponding side lengths of similar right triangles is always the same.
  • Right triangles containing identical acute anglse must be similar.

From these two relationships, you can conclude that all triangles containing an identical acute angle have the same ratio of corresponding side lengths.


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