Page 210Check for Understanding1.Two triangles can have corresponding congruentangles without corresponding congruent sides./A>/D,/B >/E, and /C >/F.However,AwBw>±DwEw,so nABC>±nDEF.2.Sample answer: In nABC,AwBwis the included sideof /A and /B.3.AAS can be proven using the Third Angle Theorem.Postulates are accepted as true without proof.4. Given:GwHwiKwJw,GwKwiHwJwProve:nGJK>nJGHProof:5. Given:XwWwiYwZw,/X>/ZProve:nWXY>nYZWProof:6. Given:QwSwbisects /RST;/R>/T.Prove:nQRS>nQTSProof:We are given that /R>/Tand QwSwbisects /RST, so by definition of angle bisector,/RSQ>/TSQ.By the Reflexive Property,QwSw>QwSw.nQRS>nQTS by AAS.7. Given:/E>/K,/DGH >/DHG,EwGw>KwHwProve:nEGD >nKHDProof:Since /EGDand /DGHare linear pairs,the angles are supplementary. Likewise,/KHDand /DHGare supplementary. We are given that/DGH>/DHG.Angles supplementary tocongruent angles are congruent so /EGD >/KHD.Since we are given that /E>/KandEwGw>KwHw,nEGD>nKHDby ASA.8.This cannot be determined. The information givencannot be used with any of the triangle congruencepostulates, theorems or the definition of congruent
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.