We know, using angle sum property of a triangle, ∠C in △ABC = 180° - (∠A + ∠B) = 180° - 135° = 45° Let us find the measure of the third angle and evaluate. Using the given measurement of angles, we cannot conclude if the given triangles follow the AA similarity criterion or not. Let us understand these steps better using an example.Įxample: Check if △ABC and △PQR are similar triangles or not using the given data: ∠A = 65°, ∠B = 70º and ∠P = 70°, ∠R = 45°. Step 3: The given triangles, if satisfy any of the similarity theorems, can be represented using the "∼" to denote similarity.Step 2: Check if these dimensions follow any of the conditions for similar triangles theorems(AA, SSS, SAS).Step 1: Note down the given dimensions of the triangles (corresponding sides or corresponding angles).We can follow the steps given below to check if the given triangles are similar or not, Two given triangles can be proved as similar triangles using the above-given theorems. In the image given below, if it is known that PQ/ED = PR/EF = QR/DFĪnd we can say that by the SSS similarity criterion, △PQR and △EDF are similar or △PQR ∼ △EDF. This criterion is commonly used when we only have the measure of the sides of the triangle and have less information about the angles of the triangle. SSS or Side-Side-Side Similarity CriterionĪccording to the SSS similarity theorem, two triangles will the similar to each other if the corresponding ratio of all the sides of the two triangles are equal. In the image given below, if it is known that AB/DE = AC/DF, and ∠A = ∠DĪnd we can say that by the SAS similarity criterion, △ABC and △DEF are similar or △ABC ∼ △DEF. ![]() This rule is generally applied when we only know the measure of two sides and the angle formed between those two sides in both the triangles respectively. SAS or Side-Angle-Side Similarity CriterionĪccording to the SAS similarity theorem, if any two sides of the first triangle are in exact proportion to the two sides of the second triangle along with the angle formed by these two sides of the individual triangles are equal, then they must be similar triangles. In the image given below, if it is known that ∠B = ∠G, and ∠C = ∠F.Īnd we can say that by the AA similarity criterion, △ABC and △EGF are similar or △ABC ∼ △EGF.Ĭlick here to understand AA Similarity Criterion in detail- AA similarity criterion 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.
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