Geometry Unit 1: Basic Geometry Geometry Unit 1: Basic Geometry · 2019. 7. 12. · angles are 1 : 3 : 5. Then list them in order from least to greatest. 13. Find the degree measure

Geometry Unit1:BasicGeometry

Ms.Talhami 1

GeometryUnit1:BasicGeometry

Name_________________


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HelpfulVocabularyWord Definition/Explanation Examples/HelpfulTips

CollinearPoints Pointsthatlieonthesameline


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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


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ClassifyingAnglesAcute Right Obtuse Straight

LabelingAnglesandSidesofTrianglesLabelingCongruentAnglesandSidesClassifyingTriangles

Acute Right Obtuse

Equilateral/Equiangular Isosceles Scalene


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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.


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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.


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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


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DevelopmentoftheExteriorAngleTheoremPractice1.

2.

3.

8.

9.

10.

14.

15.

16.


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17.

18.

19.

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


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ParallelLinesCutbyaTransversal

Note:ParallelLinescanbeinanydirectionAngleRelationshipsinParallelLinesCutbyaTransversal

TypeofRelationship AngleRelationship Examples

AlternateInteriorAngles

AlternateExteriorAngles

CorrespondingAngles

SameSideInteriorAngles

SameSideExteriorAngles


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Practice1.

2.

3.

4.

5.

6.

7.

8.

9.


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10.

11.

12.

13.

14.

15.

16.

17.

18.


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19.

20.

21.

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=________


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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


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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


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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.

3.

4.

5.

6.

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.


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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∠Cìsrepresentedbyx+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.TriangleDEFiscongruenttotriangleDÈ`F`.IfEFisrepresentedby3x+2andE`Fìsrepresentedbyx+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

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Geometry Unit 1: Basic Geometry Geometry Unit 1: Basic Geometry · 2019. 7. 12. · angles are 1 : 3 : 5. Then list them in order from least to greatest. 13. Find the degree measure