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If two parallel lines are intersected by a transversal, then prove that the bisectors of two alternate interior angles are parallel. |
| Answer» GIVEN: AB and CD are TWO parallel lines and TRANSVERSAL EF intersects then at G and H respectively. GM and HN are the bisectors of two corresponding angles ∠EGB and ∠GHD respectively.To prove: GM∥HNProof:∵AB∥CD∴∠EGB=∠GHD (Corresponding angles)⇒ 21 ∠EGB= 21 ∠GHD⇒∠1=∠2(∠1 and ∠2 are the bisector of ∠EGB and ∠GHD respectively)⇒GM∥HN(∠1 & ∠2 are corresponding angles formed by transversal GH and GM and HN and are equal.)Hence, proved.solutionStep-by-step explanation:HOPE it works | |