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.
+2440 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.
