Download 8 Justified Quest

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_____________________
__________________________________