Mathematics
1
Grade7
Geometry:Construction
Constructingaperpendicularlinewitha
compass:
Step1:PlacethecompassonpointMabovea
line
Step2:Extendcompasswidthbeyondtheline
andmaketwoarcsontheline,oneitherside
pointM.
Step3:Keepingthecompassasitis,movethe
compasstopointNandmakeasmallarc,then
movethecompasstopointOandmakeanother
smallarctoformacrossbow
Step4:ConnectpointMtothepointwherethe
twoarcsinStep3cross
MP⊥NO
ConstructingParallellinesusingacompass:
Parallellinesarelinesthatareanequaldistancefrom
eachotheratanypointonthetwolines.
Parallellinescanbeconstructedwithacompassusing
avarietyofmethods.
≫ Step5
Step6
Step3
Step1:DrawalinesegmentAB
Step4
Step2:ConstructalineCFthroughapointEonline
ABsothatCF⊥AB
Step1
≫
Step3:MarkapointDonlineCF
Step2
Step4:PlacethecompassonpointDandmaketwo
arcs(bandb1)onbothsidesofpointD
Step5:Setthecompasstobethedistancebetweenb1andb,putthecompassonpointb,
andthenb1,andmaketwocrossbowsonbothsidesofpointD
Step6:DrawalinePQthroughthecrossbowsandpointD
LinePQwillbeparalleltolineAB(AB∥PQ)
Mathematics
2
Grade7
Geometry:Construction
Locus(plural–loci)
Alocusisapaththatmovesaroundaspecificpointaccordingtosomerule.
Example:
ThelocusofapointmovesaroundpointEsothatitisatalltimesafixed
distanceawayfromthepoint.Whatshapewillitform?
Thelocuswillmoveintheshapeofacircle.
Grade7learnersneednotknowthedetailsofloci,this
justhelpstoexplainbisectinglines.
Perpendicularbisectorofaline
Perpendicularmeansalinecrossesanotherlineatanangleof90°.
Bisectormeanstocutinhalf.
ThelocusofapointthatmovessothatitisexactlythesamedistancefrompointAand
pointBoflinesegmentABwillbeaperpendicularbisectoroftheline.
Constructingaperpendicularbisector:
E
Step1:DrawalinesegmentAB
Step2:PutyourcompassonpointAanddraw
anarcoverhalfway
Step3:Keepingthecompassasitis,putthe
compassonpointBanddrawanarccrossing
thearcinStep2
Step4:DrawalinethroughpointsEandF,
wherethetwoarcsintersect
Step5:ThepointwherelineABandlineCD
meets,isthemidpointandAB⊥CD
F
Mathematics
Bisectinganangle:
3
Geometry:Construction
Whenanangleisbisected,theanglewillbedividedintotwoexactlyequalangles.
Step1:DrawananglewithavertexX
Step2:PlaceyourcompassonpointXanddrawanarcacross
bothraysoftheangle
Step3:Keepingthecompassasitis,putthecompassonpoint
Yanddrawanarcinthemiddleoftheangle
Step4:Keepingthecompassasitis,putthecompassonpoint
Zanddrawanarcinthemiddleoftheangle,crossingthearc
madeinStep3
Step5:Drawalinethroughthemiddlepointwherethetwo
arcsmeet.
AngleYXWwillnowbeequaltoangleWXZ
Practice1: Constructthefollowing,usingyourcompass:
1. ConstructMN⊥PQ,thenconstructRS∥PQ,throughpointM.
Grade7
Mathematics
4
Grade7
Practice2: Constructthefollowing:
1. Circlewitharadiusof2cm 2.
Circlewithadiameterof3cm
Practice3: Replicatethefollowingcirclepatternsonapieceofscrappaper:
Practice4:
DrawthefollowingonthecirclewithAasthecentre,thenlabeleachpart.
AREA1
AREA2
LineCD
LineEF
LineAB
Area1(formed
bylineEF)
Area2(formed
bylineABand
AD)
Mathematics
5
Practice5: Constructthefollowingangles:
1. ∠𝐴𝐵𝐶 = 38° 3. ∠𝑀𝑁𝑂 = 192°
5. Bisectangle∠𝐷𝐸𝐹 = 60° Grade7
2.
∠𝑃𝑄𝑅 = 106°
4.
∠𝐴𝐵𝐶 = 280°
6.
Bisectangle∠𝐻𝐼𝐽 = 88°
Mathematics
6
Grade7
MEMO:
Practice1: Constructthefollowing,usingyourcompass:
1. ConstructPQ∥RS.DrawapointMonlineRS,thenconstructMN⊥PQ.
(Compassmarksnotshownonthisconstruction–refertopage1forinstructions)
≫
≫
Practice2: Constructthefollowing:
1. Circlewitharadiusof2cm 2.
Circlewithadiameterof3cm
Practice3:
(Notdrawntoscale)
Replicatethefollowingcirclepatternsonapieceofscrappaper:
Mathematics
Practice4:
7
Grade7
DrawthefollowingonthecirclewithAasthecentre,thenlabeleachpart:
LineCD
diameter
LineEF
chord
LineAB
radius
Area1(formed
bylineEF)
Area2(formed
bylineABand
AD)
segment
sector
Practice5: Constructthefollowingangles:(Variancesof2°eitherwayallowed)
1. ∠𝐴𝐵𝐶 = 38° 2.
∠𝑃𝑄𝑅 = 106°
EastofNorth(right-facing) 3. ∠𝑀𝑁𝑂 = 192°
5.
WestofNorth(left-facing)
Bisectangle∠𝐷𝐸𝐹 = 60°
Bisector=EG EastofNorth(right-facing)
4.
∠𝐴𝐵𝐶 = 280°
6.
WestofNorth(left-facing)
Bisectangle∠𝐻𝐼𝐽 = 88°
Bisector=IK