Similarity is the relation of equivalence. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. AAS (angle-angle-side) What are the conditions for similarity? When you’ve got two triangles and the ratio of two of their sides are the same, plus one of their angles are equal, you can prove that the two triangles are similar.ĪSA (angle-side-angle) Two angles and the side between them are congruent. The SAS similarity theorem stands for side angle side. The fundamental theorem of similarity states that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle’s third side. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. These three theorems, known as Angle – Angle (AA), Side – Angle – Side (SAS), and Side – Side – Side (SSS), are foolproof methods for determining similarity in triangles. When the three angle pairs are all equal, the three pairs of sides must also be in proportion. We know this because if two angle pairs are the same, then the third pair must also be equal. If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. If two triangles have two of their angles equal, the triangles are similar. AA stands for “angle, angle” and means that the triangles have two of their angles equal. AA Similarity Postulate: If two angles in one triangle are congruent to two angles in another triangle, then the two triangles are similar.
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