The three triangle similarity theorems are SSS, SAS, and ASA. What are the 3 triangle similarity theorems? ASA means "angle, side, angle," SSS means "side, side, side," AAS means "angle, angle, side," and SAS means "side, angle, side." SSS means "side, side, side," SAS means "side, angle, side," ASA means "angle, side, angle," and AAS means "angle, angle, side." I-AL is an acronym for "image and line." It refers to two figures that are similar because they have the same shape, but not necessarily the same size.ĪSA, SSS, AAS, and SAS are all types of similarity. SSS, SAS, ASA, and AAS are all types of similarity. This theorem is also known as the AAA similarity theorem. In other words, if two angles are equal in measure, then they are equal in shape. The angle similarity theorem states that if two angles have the same measure, then they are similar. Once we know these things are true, we can use proportions to solve for missing lengths in similar triangles.įAQ What is the angle similarity theorem? In order for two triangles to be considered similar by the AAS Similarity Theorem, corresponding angles must be congruent and the lengths of corresponding sides must be proportional. The AAS Similarity Theorem provides a way for us to determine whether two triangles are similar. This proportionality relationship allows us to set up and solve proportions to find missing lengths. Then, we can say that AB is to XY as BC is to YZ as AC is to XZ. What this means is that if we label the sides of Triangle ABC as follows: Side AB is side XY, Side BC is side YZ, and Side AC is side XZ. The lengths of corresponding sides are proportional. In other words, angle 1 in Triangle ABC must be equal to angle 1 in Triangle XYZ, angle 2 in Triangle ABC must be equal to angle 2 in Triangle XYZ, and so on. In order for two triangles to be similar by the AAS Similarity Theorem, the following must be true:Ĭorresponding angles are congruent. The Angle-Angle-Side (AAS) Similarity Theorem is a way to determine if two triangles are similar. In geometry, two shapes are similar if they have the same shape, but not necessarily the same size.
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