Choose the letter of the word or phrase that best completes each statement: If ∠ A ≅ ∠ X and A B X Y = A C X Z , then △ A B C ∼ △ X Y Z by the __________. Choose from: a. scale factor, b. AA Similarity Postulate, c. SSS Similarity Theorem, d. SAS Similarity Theorem, e. Symmetric Property of Similarity, f. midsegment, g. dilation, h. enlargement, i. reduction, j. Transitive Property of Similarity

Question

Choose the letter of the word or phrase that best completes each statement: If   ∠  A  ≅  ∠  X and             A      B              X      Y        =            A      C              X      Z      , then   △  A  B  C  ∼  △  X  Y  Z by the __________. Choose from: a. scale factor, b. AA Similarity Postulate, c. SSS Similarity Theorem, d. SAS Similarity Theorem, e. Symmetric Property of Similarity, f. midsegment, g. dilation, h. enlargement, i. reduction, j. Transitive Property of Similarity

Harper Brewer · Accepted Answer

∠  A is the included angle of             A      B        ¯   and             A      C        ¯   and   ∠  X is the included angle of             X      Y        ¯   and             X      Z        ¯  .Therefore if             A      B              X      Y        =            A      C              X      Z      , then   △  A  B  C  ∼  △  X  Y  Z by the SAS Similarity Theorem since the triangles have two pairs of proportional corresponding sides and a pair of congruent included angles. The correct answer is then d. SAS Similarity Theorem.Result:d

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