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Good Luck To: _____________________________ On My Honor I pledge that I have not and will not violate the Honor Code: __________________________ JustifiedQuest Geometry (38points) Besuretogivethegeometricjustification(theorem,postulate,property,definition)forthe equationthatyousetupandtoshowallyouralgebraicwork. 1. Calculatethevalueofxgiventhediagrambelow.(4pts.) 2. Calculate m∠1, m∠2, and m∠3 usingthediagramtotheleft.(6pts.) 3. Nameapairofcomplementaryanglesinthediagramtotheright.(1pts.) 4. Nameapairofverticalanglesinthediagramtotheright.(1pts.) 5. The measure of an angle is equal to 6 less than 3 times its complement. Find the angle (x) and its complement. (4 points) a. x = ________________ b. Complement of x = _______________ 6. Matcheachpropertybelowwiththecorrespondingexamplefromtheright-handcolumn. (1pt.each) Pleasenotice:therearemoreexamplesthanproperties! A.If 3x = 5 ,then 9x = 15 . ______ReflexiveProperty B.If x = 5 and 3x = 2y ,then 3(5) = 2y . ______AdditionProperty C.If x = y and b = d ,then x + b = y + d . ______DistributiveProperty D.If ∠1 ≅ ∠3 and ∠3 ≅ ∠4 ,then ∠1 ≅ ∠4 . ______TransitiveProperty E.If 4x = 2 ,then 2 = 4x . ______SubstitutionProperty F.If 8x + 4 = 20 ,then 2x + 1 = 5 . ______MultiplicationProperty G.IfTW=HGandLK=ND,thenTW–LK=HG–ND. ______DivisionProperty H. m∠4 = m∠4 I. 3( x + 5 ) = 3x + 15 J. ( x + 2 ) + 7 = x + ( 2 + 7 ) !##" !##" 7. Given AB ⊥ CD ,statethetheoremordefinitionthatjustifiesthefollowingstatements.(3pts.) a. ∠8 isa90ºangle b. ∠7 ≅ ∠10 c. ∠9 and ∠10 arecomplementary 8. Fillinthemissingstatementsandreasonsforthetwo-columnproofbelow.(6points) Given: <ODE is a right angle. Prove: <ODV and <VDE are complementary. 1. _________________________________ 1. Angle Addition Postulate 2. ________________________________ 2. Given 3. <ODE = 90. 3. __________________________ 4. _________________________________ 4. Transitive POE (from steps 1 and 3) 5. _________________________________ 5. __________________________________ 9. Fillinthemissingstatementsandreasonsforthetwo-columnproofbelow.(6points) Statements Reasons 1. ∠3 ≅ ∠2 1.________________________________ !!!" 2. BD bisects ∠ABC 3. ∠2 ≅ ∠1 2._______________________________ 4.____________________ 4.VerticalAnglesTheorem 5.________________________________ 5.TransitivePropertyofCongruence 6.________________________________ 6.definitionofanglebisector 3.definitionof_____________________ __________________________________