AMSCO'S Geometry. New York - Rye High School

338 Parallel Linesc. Since GHC and GHD form a linear pair and are supplementary,mGHD 180 mGHC 180 70 110Answers a. x 70 b. mGHC 70 c. mGHD 110Using Theorem 9.1, we may also prove the following theorems:Theorem 9.6 If a transversal is perpendicular to one of two parallel lines, it is perpendicularto the other.EGiven AB g CD g, EF g⊥ AB gABProveEF g⊥ CD gCFDStrategyShow that alternate interior angles are right angles.The proof of this theorem is left to the student. (See exercise 19.)Theorem 9.7If two of three lines in the same plane are each parallel to the third line, thenthey are parallel to each other.GivenProveAB g LM gand CD g LM gAB g CD gProof Draw transversal intersecting LM g AgEJGMat H. Since AB g LM g, this transversalalso intersects AB gCH. Call this point F.JSimilarly, since CD g LM g, this transversalalso intersects CD gat a point G.LSince AB g LM g , alternate interior angles formed are congruent. Therefore,AFG GHM. Similarly, since CD g LM g, CGH GHM. By the transitiveproperty of congruence, AFG CGH. Angles AFG and CGH are congruentcorresponding angles when AB gand CD gare intersected by transversalEFBD