# Homework 9 page 54.pdf - Homework 9 54: 3, 6 and 58: 7, 9...

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Homework 954: 3, 6 and58: 7, 9Page 54#3.If two Saccheri quadrilaterals have equal arms and unequal bases, prove that the onewith the greater base has smaller summit angles. (Use Ex. 2 and Theo. 39).Consider Saccheri quadrilateralsABCDandPQRS,givenBC = DA= QR = SPas shown and WLOG letPQ > AB.LocateTonPQsuchthatAB = PT,and constructTUperpendicular toPQ.By Theorem39,UTSP.(wlog it can be on the left side of the perpendicular)Thus by substitutionUTBC.LocateEonBCsuch thatBE = TU.ThenABEDis congruent toPTUSby ex. 6 on page 44. Then mPSU= mADE. Since mADE = mADC, it follows that mPSU = mADC.#6 Prove that two lines have a common perpendicular if there is a transversal such that thatthe sum of the two interior angles on the same side of the transversal it 180°.

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