41. Given:nABCProve:m/CBD5m/A1m/CProof:42. Given:nRST/Ris a right angleProve:/S and /Tare complementaryProof:43. Given:nMNO/Mis a right angle.Prove:There can be atmost one right angle in a triangle.Proof:In nMNO,/Mis a right angle.m/M 1m/N1m/O5180.m/M590, som/N1m/O590. If /N were a right angle,then m/O50. But that is impossible, so therecannot be two right angles in a triangle.Given:nPQR/P is obtuse.Prove:There can be at most one obtuse angle ina triangle.Proof:In nPQR,/Pis obtuse. So m/P .90.m/P1m/Q1m/R5180. It must be that m/Q1m/R,90. So,/Qand /Rmust beacute.44. Given:/A >/D/B >/EProve:/C >/FProof:45.m/11m/21m/35¬1804x15x16x5¬18015x5¬180x5¬12m/154(12) or 48m/255(12) or 60m/356(12) or 72 46.Sample answer: The shape of a kite is symmetric. Iftriangles are used on one side of the kite, congruenttriangles are used on the opposite side. The wingsof this kite are made from congruent righttriangles. Answers should include the following.
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