Geometry Unit1:BasicGeometry
Ms.Talhami 1
GeometryUnit1:BasicGeometry
Name_________________
Geometry Unit1:BasicGeometry
Ms.Talhami 2
HelpfulVocabularyWord Definition/Explanation Examples/HelpfulTips
CollinearPoints Pointsthatlieonthesameline
Geometry Unit1:BasicGeometry
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FrequentlyUsedGeometricNotationsGeometricSymbol Interpretation Example
Angle
Triangle
Point
Line
LineSegment
TheMeasureOf
Ray
Parallel
Perpendicular
Congruent
Similar
GeometricLabeling
Figure ExamplesofLabeling Non-ExamplesofLabeling
LinesSegments
Rays
Angles
ClosedFigures
Geometry Unit1:BasicGeometry
Ms.Talhami 4
ClassifyingAnglesAcute Right Obtuse Straight
LabelingAnglesandSidesofTrianglesLabelingCongruentAnglesandSidesClassifyingTriangles
Acute Right Obtuse
Equilateral/Equiangular Isosceles Scalene
Geometry Unit1:BasicGeometry
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AnglesofTriangles
Practice1.
m∠C=_______
2.m∠C=_______
3.x=_________
4.x=______m∠A=_______
5.x=______m∠B=_______
6.x=_________
7.x=_________
8.Ifthemeasuresoftheanglesofatrianglearerepresentedby3x,5x-20and4x+10.Findthemeasuresofthethreeangles.
Geometry Unit1:BasicGeometry
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9.Themeasureofthelargestangleinatriangleis4timesthemeasureofthesecondlargestangle.Thesmallestangleis10°.Whatarethemeasuresofalltheangles?
10.InΔABC,themeasureof∠Aisone-halfthemeasureof∠Bandthemeasureof∠Cisthreetimesthemeasureof∠B.Findthemeasuresofeachangle.
11.InΔPQR,themeasureof∠Pistwicethemeasureofangle∠Q.Themeasureof∠Risthreetimesthemeasure∠P.Findthemeasuresofeachangle.
12.Findthedegreemeasureofeachangleofatriangleiftheratioofthemeasuresofthethreeanglesare1:3:5.Thenlisttheminorderfromleasttogreatest.
13.Findthedegreemeasureofeachangleofatriangleiftheratioofthemeasuresofthethreeanglesare1:4:7.Thenlisttheminorderfromleasttogreatest.
Geometry Unit1:BasicGeometry
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MoreVocabularyWord Definition/Explanation Examples/HelpfulTips
ComplementaryAngles
SupplementaryAngles
LinearPair
VerticalAngles
Practice1.
m∠b=_______
2.m∠b=_______
3.b=_______
4.
x=_______
5.x=_______
6.x=_______
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7.b=_______
8.x=_______
9.x=_______
10.x=_______
11.x=_______
12.x=_______
13.x=_______
14.x=_______
15.x=_______
16.
x=_______y=_______
17.Ifm<FTE=58°,findthemeasuresofalltheremainingangles.
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18.Basedonthediagram,arethefollowingtrueorfalse?a)∠5and∠3areverticalanglesTorFb)∠1and∠5arealinearpairTorFc)∠4and∠3areadjacentanglesTorFd)∠4and∠1areverticalanglesTorFe)∠3and∠4arealinearpairTorF19.If∠Aand∠Baresupplementsandm∠A=150o,whatism∠B?
20.If∠Aand∠Barecomplementsandm∠A=27o,whatism∠B?
21.If∠Aand∠Bareverticalanglesandm∠A=36o,whatism∠B?
22.If∠Aand∠Barealinearpairandm∠A=2x+8andm∠B=3x+2,whatisthevalueofx?
23.Ifm∠A=7x-5andm∠B=4x+10and∠Aand∠Bareverticalangles,whatisthevalueofx?
24.m∠A=______m∠C=______
25.x=______m∠C=______
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26.x=______
27.x=______
28.x=______
29.x=______
30.m∠1=______m∠2=______m∠3=______
31.m∠1=______m∠2=______m∠3=______
ExteriorAngleTheorem
Word Examples Non-Examples
ExteriorAngle
Geometry Unit1:BasicGeometry
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DevelopmentoftheExteriorAngleTheoremPractice1.
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8.
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14.
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16.
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17.
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20.Findthemeasureofeitheroftheexterioranglesformedbyextendingthebaseofanisoscelestriangle,ifthevertexangleofthetriangleis20.
28.InΔPQR,themeasureof∠Pistwicethemeasureof∠Q.Ifanexteriorangleatvertex∠Rhasadegreemeasureof120,findm∠Q
Findthemeasureofeitheroftheexterioranglesformedbyextendingthebaseofanisoscelestriangle,ifthevertexangleofthetriangleis135.
29.InΔABC,m∠Bisfourtimesaslargeasm∠A.Anexteriorangleat∠Cmeasures125.Findthedegreesm∠A.
ParallelLines
Word Definition/Explanation Examples/HelpfulTips
ParallelLines
TransversalLine
Geometry Unit1:BasicGeometry
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ParallelLinesCutbyaTransversal
Note:ParallelLinescanbeinanydirectionAngleRelationshipsinParallelLinesCutbyaTransversal
TypeofRelationship AngleRelationship Examples
AlternateInteriorAngles
AlternateExteriorAngles
CorrespondingAngles
SameSideInteriorAngles
SameSideExteriorAngles
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Practice1.
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9.
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10.
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18.
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19.
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22. a)∠1=∠4 TorF b)∠3=∠5 TorF c)∠2=∠10 TorF d)∠12=∠14 TorF e)∠9=∠11 TorF f)∠9=∠15 TorF g)∠6=∠16 TorF h)∠4=∠5 TorF i)m∠11+m∠15=180oTorF j)m∠1+m∠8=180o TorF13.x=_________y=________
14.x=_________y=________
Geometry Unit1:BasicGeometry
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TriangleInequalityTheoremPractice
Tellwhetherthegivenlengthsmaybethemeasureofthesidesofatriangle.1.3,4,5 2.5,8,13 3.6,7,10 4.3,9,15 5.2,2,3
6.1,1,2 7.3,4,4 8.5,8,11 9.6,2,3 10.5,3,7
TriangleInequalityTheoremDiscovery
Geometry Unit1:BasicGeometry
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PracticeUsingtheDiscovery
Tellwhetherthegivenlengthsmaybethemeasureofthesidesofatriangle.11.4,6,3
12.9,4,5
13.2,3,5
14.4,4,8
15.3,4,8
16.5,6,7
17.6,10,9
18.7,5,8
19.6,13,7
20.2,5,3
MorePractice1.Whichsetofnumberscouldnotbethelengthsofthesidesofatriangle?1)1,1,22)2,3,43)1, ,24)3,4,5
2.Whichsetofnumberscouldnotbethelengthsofthesidesofatriangle?1)4,7,92)4,8,123)9,10,114)6,6,11
3.Whichsetofnumberscouldnotbethelengthsofthesidesofatriangle?1)9,12,192)6,8,113)7,18,114)7,5,6
4.Whichsetofnumberscouldbethelengthsofthesidesofaisoscelestriangle?1)15,5,102)3,4,53)1,1,34)6,6,5
5.Twosidesofanisoscelestrianglehavelengths2and12respectively.Whatisthelengthofthethirdside?1)92)83)124)14
6.Twosidesofanisoscelestrianglehavelengths4and8.Whatisthethirdside?1)42)63)54)8
7.Twosidesofatrianglehavelengths5and8.Whichlengthcannotbethelengthofthethirdside?1)52)43)34)6
8.Twosidesofatrianglehavelengths4and7.Whichlengthcannotbethelengthofthethirdside?1)112)53)74)4
Geometry Unit1:BasicGeometry
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TriangleLargestandSmallestAnglesandSides
Practice1.InΔDNA,find:a)smallestangle______b)largestangle______
2.InΔSUE,find:a)smallestangle______b)largestangle______
3.InΔAME,find:a)smallestside______b)largestside______
4.InΔNES,find:a)smallestside______b)largestside______
5.InΔZPA,find:a)smallestside______b)largestside______
6.InΔFCX,find:a)smallestside______b)largestside______
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7.Onthebanksofariver,surveyorsmarkedlocationsA,B,andC.Themeasureof∠ACE=70°andthemeasureof∠ABC=65°.
Whichexpressionshowstherelationshipbetweenthelengthsofthesidesofthistriangle?1) AB<BC<AC2) BC<AB<AC3) BC<AC<AB4) AC<AB<BC
8.InΔPQR, , ,and .WhichstatementabouttheanglesofΔPQRmustbetrue?1) 2) 3) 4)
9.InΔABC,∠A≅∠Bandm∠Cisanobtuseangle.Whichstatementistrue?1) and isthelongestside.2) and isthelongestside.3) and istheshortestside.4) and istheshortestside.
10.InΔABC,m∠A=60o,m∠B=80o, ,andm∠C=40o.Whichinequalityistrue?1) AB>BC2) AC>BC3) AC<BA4) BC<BA
11.InΔABC, , ,and.DeterminethelongestsideofΔABC.
12.AsshowninthediagramofΔACDbelow,Bisapointon and isdrawn.
If , ,and ,whatisthelongestsideofΔABD?1) 2) 3) 4)
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PolygonsWord Definition/Explanation Examples/HelpfulTips
Polygon
RegularPolygon
IdentifyingPolygonsNameeachpolygon1.
2.
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7.
ExteriorAnglesofPolygons
Word Examples Non-Examples
ExteriorAnglesofPolygons
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ExteriorAnglesofPolygonsDiscoveryPractice1.Thepentagoninthediagrambelowisformedbyfiverays.Whatisthedegreemeasureofanglex?1) 722) 963) 1084) 112
2.Astopsignintheshapeofaregularoctagonisrestingonabrickwall,asshownintheaccompanyingdiagram.Whatisthemeasureofanglex?1) 45°2) 60°3) 120°4) 135°
3. Whichregularpolygonhasaminimumrotationof45°tocarrythepolygonontoitself?1) octagon2) decagon3) hexagon4) pentagon
4.Aregularhexagonisrotatedinacounterclockwisedirectionaboutitscenter.Determineandstatetheminimumnumberofdegreesintherotationsuchthatthehexagonwillcoincidewithitself.
Geometry Unit1:BasicGeometry
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InteriorAnglesofPolygonsDiscoveryDeterminetheSumoftheInteriorAnglesofEachFigure1.
2.
3.
4.
Practice1.Whatisthemeasureofeachinteriorangleinaregularoctagon?1) 108º2) 135º3) 144º4) 1080º
2.Thesumoftheinterioranglesofaregularpolygonis540°.Determineandstatethenumberofdegreesinoneinteriorangleofthepolygon.
3.Themeasureofaninteriorangleofaregularpolygonis108°.Whatisthenameofthepolygon?
4.Themeasureofaninteriorangleofaregularpolygonis120°.Howmanysidesdoesthepolygonhave?1) 52) 63) 34) 4
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MixedReviewQuestions1.InthediagramofparallelogramFREDshownbelow, isextendedtoA,and isdrawnsuchthat .If ,whatis ?1) 124°2) 112°3) 68°4) 56°
2.InparallelogramQRSTshownbelow,diagonal isdrawn,UandVarepointson and ,respectively,and intersects atW.If
, ,and ,whatis?
1) 37º2) 60º3) 72º4) 83º
3.Inthediagrambelow, , ,and .Whichstatementistrue?1) isobtuse.2) isisosceles.3) 4) isscalene.
4.StevedrewlinesegmentsABCD,EFG,BF,andCFasshowninthediagrambelow.Scalene isformed.WhichstatementwillallowStevetoprove
?1) 2) 3) 4)
5.Inthediagrambelow, intersects and atGandH,respectively,and isdrawnsuchthat
.If and ,explainwhy .
6.Inthediagrambelow,lines ,m,n,andpintersectliner.Whichstatementistrue?1) 2) 3) 4)
7.InthediagrambelowofisoscelestriangleABC, andanglebisectors , ,and aredrawnandintersectatX.If ,find .
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8.ThediagrambelowshowsΔABD,withABC,BE⊥AD,and∠EBD=∠CBD.
Ifm∠ABE=52o,whatism∠D?1) 262) 383) 524) 64
9.InthediagramofΔJEAbelow,m∠JEA=90oandm∠EAJ=48o.LinesegmentMSconnectspointsMandSonthetriangle,suchthatm∠EMS=58o.
Whatism∠JSM?1) 1632) 1213) 424) 17
10.TheanglesoftriangleABCareintheratioof8:3:4.Whatisthemeasureofthesmallestangle?1) 12º2) 24º3) 36º4) 72º
11.Inanequilateraltriangle,whatisthedifferencebetweenthesumoftheexterioranglesandthesumoftheinteriorangles?1) 180°2) 120°3) 90°4) 60°
12.TrianglePQRhasanglesintheratioof2:3:5.WhichtypeoftriangleisΔPQR?1) acute2) isosceles3) obtuse4) right
13.InΔABC,m∠A=3x+1,m∠B=4x-17,andm∠C=5x-20.WhichtypeoftriangleisΔABC?1) right2) scalene3) isosceles4) equilateral
14.InΔABC,m∠A=x,m∠B=2x+2,andm∠C=3x+4.Whatisthevalueofx?1) 292) 313) 594) 61
15.InΔDEF,m∠D=3x+5,m∠E=4x-15,andm∠F=2x+10.Whichstatementistrue?1) DF=FE2) DE=FE3) m∠E=m∠F4) m∠D=m∠F
16.JuliannplansondrawingΔABC,wherethemeasureofm∠Acanrangefrom50°to60°andthemeasureofm∠Bcanrangefrom90°to100°.Giventheseconditions,whatisthecorrectrangeofmeasurespossibleform∠C?1) 20°to40°2) 30°to50°3) 80°to90°4) 120°to130°
17.ThedegreemeasuresoftheanglesofΔABCarerepresentedbyx,3x,and5x-24.Findthevalueofx.
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18.Whatisthemeasureofthelargestangleintheaccompanyingtriangle?
1) 412) 46.53) 564) 83
19.Abillboardonlevelgroundissupportedbyabrace,asshownintheaccompanyingdiagram.ThemeasureofangleAis15°greaterthantwicethemeasureofangleB.DeterminethemeasureofangleAandthemeasureofangleB.
20.InrighttriangleABC,m∠C=3y–10,m∠B=y+40,andm∠A=90.WhattypeofrighttriangleistriangleABC?1) scalene2) isosceles3) equilateral4) obtuse
21.Ifthemeasuresoftheanglesofatrianglearerepresentedby2x,3x–15,and7x-15thetriangleis1) anisoscelestriangle2) arighttriangle3) anacutetriangle4) anequiangulartriangle
22.Ifthemeasures,indegrees,ofthethreeanglesofatrianglearex,x+10and2x–6,thetrianglemustbe1) isosceles2) equilateral3) right4) scalene
23.Ifthevertexanglesoftwoisoscelestrianglesarecongruent,thenthetrianglesmustbe1)acute2)congruent3)right4)similar
24.Theaccompanyingdiagramshowstheroofofahousethatisintheshapeofanisoscelestriangle.Thevertexangleformedatthepeakoftheroofis84°.
Whatisthemeasureofx?1)138°2)96°3)84°4)48°
25.Tinawantstosewapieceoffabricintoascarfintheshapeofanisoscelestriangle,asshownintheaccompanyingdiagram.
Whatarethevaluesofxandy?1)x=42andy=962)x=69andy=693)x=90andy=484)x=96andy=42
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26.Intheaccompanyingdiagram,isoscelesΔABC≅isoscelesΔDEF,m∠C=5x,andm∠D=2x+18.Findm∠Bandm∠BAG.
27.Intheaccompanyingdiagram,ΔABCandΔABDareisoscelestriangleswithm∠CAB=50andm∠BDA=55.IfAB=ACandAB=BD,whatism∠CBD?
28.InisoscelestriangleDOG,themeasureofthevertexangleisthreetimesthemeasureofoneofthebaseangles.WhichstatementaboutΔDOGistrue?1)ΔDOGisascalenetriangle.2)ΔDOGisanacutetriangle.3)ΔDOGisarighttriangle.4)ΔDOGisaobtusetriangle.
29.VertexangleAofisoscelestriangleABCmeasures20°morethanthreetimesm∠B.Findm∠C.
30.Herschsaysifatriangleisanobtusetriangle,thenitcannotalsobeanisoscelestriangle.Usingadiagram,showthatHerschisincorrect,andindicatethemeasuresofalltheanglesandsidestojustifyyouranswer.
31.InΔABC,themeasureofm∠Bis21lessthanfourtimesthemeasureofm∠A,andthemeasureofm∠Cis1morethanfivetimesthemeasureofm∠A.Findthemeasure,indegrees,ofeachangleof
32.TriangleABCiscongruenttotriangleA`B`C`.Ifm∠Cisrepresentedby2x–10andm∠C`isrepresentedbyx+30:a)Findxb)Findthem∠Cc)Findm∠Bifitisrepresentedbyx-25
33.InisoscelestriangleABC,AB=BC.Whichstatementwillalwaysbetrue?1) m∠B=m∠A2)m∠A>m∠B3) m∠A=m∠C4)m∠C<m∠B
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34.TriangleDEFiscongruenttotriangleD`E`F`.IfEFisrepresentedby3x+2andE`F`isrepresentedbyx+10andEDisrepresentedbyx+2:a)findx,b)FindEDc)FindE`D`d)FindEF
35.GiventhatAD≅CBand∠1≅∠2andAB=5x–3,CD=3x+10andBC=2x+5,writeanequationtosolveforx,andthenfindAB,CD,andBC.
36.IfΔABC,BDisthemediantosideACandmustbecongruentifΔABDInΔABCΔCBD,thenΔABCmustbe1)scalene2)isosceles3)right4)equilateral
37.Tworighttriangles:1)Thehypotenuseofonetriangleiscongruenttothehypotenuseoftheother.2)Anacuteangleofonetriangleiscongruenttoanacutetriangleoftheother.3)Twolegofonetrianglearecongruenttotwolegsoftheother.4)Eachcontainsarightangle.
38.Twoisoscelestrianglesarecongruentif1)Thevertexangleofonetriangleiscongruenttothevertexangleoftheother.2)Abaseangleofonetriangleiscongruenttoabaseanglesoftheother.3)Legofonetriangleiscongruenttoalegoftheother4)Alegandvertexangleofonetrianglearecongruenttoalegandvertexangleoftheother.
39.InΔABC,DisapointonBCsuchthatADisbothanglebisectorandanaltitudeinΔABC.Whichstatementmaybefalse?1)BD=CD2)AB=AC3)AC=BC4)m∠B=m∠C