![]() ![]() Example 2 Let the vertices of triangles ABC and PQR defined by the coordinates: A (-2,0), B (0,4), C (2,0), P (-1,1), Q (0,3), and R (1,1). SAS Similarity Theorem The Side-Angle-Side (SAS) Similarity Theorem states that if an angle of one triangle is con- gruent to an angle ofa second triangle. Using Theorem 6.2 : If a line divides any two sides of a triangle in the same ratio, then the line is parallel to third side. Side-Side-Side (SSS) Similarity Theorem If the three sides of a triangle are proportional to the corresponding sides of a second triangle, then the triangles are similar. Such that DP = AB and DQ = AC respectively If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including. ![]() ![]() Given: Two triangles ∆ABC and ∆DEF such that Side-Angle-Side (SAS) Similarity Theorem. SAS similarity theorem- if an angle of one triangle is congruent to an angle of a seond triangle and the lengths of the sides including these angles are. SAS Similarity theorem states that, If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent. Theorem 6.5 (SAS Criteria) If one angle of a triangle is equal to one angle of the other triangle and sides including these angles are proportional then the triangles are similar. Follow the plan for proof of SAS Similarity Theorem and SSS Similarity Theorem to explain why the theorems are true. ![]()
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