AA similarity rule is easily applied when we only know the measure of the angles and have no idea about the length of the sides of the triangle. AA (or AAA) or Angle-Angle Similarity CriterionĪA similarity criterion states that if any two angles in a triangle are respectively equal to any two angles of another triangle, then they must be similar triangles. Let us understand these similar triangles theorems with their proofs. SSS or Side-Side-Side Similarity Theorem.SAS or Side-Angle-Side Similarity Theorem.AA (or AAA) or Angle-Angle Similarity Theorem.There are three major types of similarity rules, as given below, These similar triangle theorems help us quickly find out whether two triangles are similar or not. We use these similarity criteria when we do not have the measure of all the sides of the triangle or measure of all the angles of the triangle. We can find out or prove whether two triangles are similar or not using the similarity theorems. The following image shows similar triangles, but we must notice that their sizes are different. Therefore, all equilateral triangles are examples of similar triangles. That means equiangular triangles are similar. Similar triangles are triangles for which the corresponding angle pairs are equal. So, if two triangles are similar, we show it as △QPR ∼ △XYZ Similar Triangles Examples We use the "∼" symbol to represent the similarity. All corresponding sides of triangles are proportional.All corresponding angle pairs of triangles are equal.Similar triangles may have different individual lengths of the sides of triangles but their angles must be equal and their corresponding ratio of the length of the sides must be the same. Two triangles will be similar if the angles are equal ( corresponding angles) and sides are in the same ratio or proportion( corresponding sides). This property of similar shapes is referred to as " Similarity". That means similar shapes when magnified or demagnified superimpose each other. Two objects can be said similar if they have the same shape but might vary in size. Similar triangles are the triangles that look similar to each other but their sizes might not be exactly the same.
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