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Is ∆GHI ~∆KLM?If so by what Similarity Postulate or Theorem.

Question  options:

No, ∆GHI is not similar to ∆KLM.

Yes ∆GHI ~∆KLM by SSS Similarity

Yes ∆GHI ~∆KLM by SAS Similarity. 

Yes ∆GHI ~∆KLM by AA Similarity.

 Jun 3, 2018

By the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary, so \(m\angle IGH+m\angle GHI=90^{\circ}\)\(m\angle IGH=32^{\circ}\) is given information. Because \(m\angle IGH=32^{\circ}\)\(32^{\circ}\) can replace \(m\angle IGH\) in the previous equation, according to the Substitution Property of Equality, which results in the univariate equation \(32^{\circ}+m\angle GHI=90^{\circ}\) . Using the Subtraction Property of Equality in conjunction with simplifying, \(m\angle GHI=58^{\circ}\)\(\angle HIG \cong \angle LMK\) by the Right Angle Congruence Theorem. Because \(m\angle GHI=58^{\circ}\) and \(m\angle KLM=58^{\circ}\) , the Definition of Congruent Angles concludes that \(\angle GHI\cong \angle KLM\)\(\angle HIG \cong \angle LMK\) and \(\angle GHI\cong \angle KLM\) are examples of two pairs of corresponding congruent angles, so, yes, \(\triangle GHI\sim\triangle KLM\) by the AA Similarity Theorem.

 Jun 3, 2018

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