chapter 1 basics of geometry ch 1.1 points, lines and planesgreenstein.com/mvhs/geom/lessons/big...
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BigIdeasCh1Notes
Geometry Name___________________________________________ Date____________________________Period__________
Chapter1BasicsofGeometry
Ch1.1Points,LinesandPlanes
UndefinedTerms:1)
2)
3)
Pointsthatlieonthesamelinearecalled___________________________________________________
Pointsthatlieonthesameplanearecalled___________________________________________________
DefinedTerms:1)
2)
3)
Intersec>ons:
Theintersec>onoftwodifferentlinesisa_________________________________.�
Theintersec>onoftwodifferentplanesisa_________________________________.�
Usethediagramandiden>fyexamplesofthefollowing:1)asegment2)aplane3)intersec>onlines4)intersec>ngplanes5)apointnotinaplane6)alinenotinaplane
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BigIdeasCh1Notes
Always,SomeBmes,Never
1)Aline____________________________hasendpoints.
2)Alineandapoint____________________________intersect.
3)Aplaneandapoint____________________________intersect.
4)Twoplanes____________________________intersectinaline.
5)Anythreepoints____________________________determinesaplane.
6)Twolinesthatarenotparallel____________________________intersect.
Ch1.2MeasuringandConstrucBngSegments
Postulate:_______________________________________________________________________________________________
Theorem:________________________________________________________________________________________________
_________________________________________________________________________
Distance:___________________________________________________________________________
Congruentsegments:_______________________________________________________________________
Between:_______________________________________________________________________
Segment Addition Postulate
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BigIdeasCh1Notes
Ch1.3UsingMidpointandDistanceFormulas
Midpoint:___________________________________________________________________________________________________
SegmentBisector:_____________________________________________________________________________________________
Example:
x= PM=
MidpointFormula
___________________________________________________________________________
Computethefollowing.1)MidpointofA(1,2)andB(7,8)
2)MidpointofC(-4,3)andD(-6,5)
3)ThemidpointofasegmentVWisM(-1,-2)andoneendpointisW(4,4).DeterminethecoordinateofV.
DistanceFormula
AB=
Example:Computethedistancebetweenthefollowingpoints:
(x1,y1)=(2,3)
(x2,y2)=(4,-1)
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M( , )
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BigIdeasCh1Notes
Ch1.4PerimeterandAreaintheCoordinatePlane
Proper>esofaPolygon:
ConvexPolygon: ConcavePolygon:
Classifythesepolygonsbytypeandconvexorconcave:1) 2) 3) 4)
� � � �
PerimeterandArea
� � � P= P= P=
A= A= A=
NumberofSides
TypeofPolygon NumberofSides
TypeofPolygon
3 8
4 9
5 10
6 12
7 n
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BigIdeasCh1Notes
Example:Calculatetheperimeterandareaofthefigureontheright.
Example:CalculatetheperimeterandareaofthequadrilateralEFGH,inwhichE(-3,6),F(-7,3),G(-1,-5),H(3,-2).
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Ch1.5MeasuringandConstrucBngAngles
Vocabulary
angle:
angleinterior:
NaminganangleUsethevertex:
Useapointoneachrayandthevertex:
Useanumber:
ExamplesofAmbiguousanglename:
Unambiguousanglename:
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BigIdeasCh1Notes
MeasureofanAngle
Themeasureof___________________,alsowri^en___________________,isthedifferenceof
theanglesoftherays___________and_______________onaprotractor.
TypesofAnglesacute:
right:
obtuse:
straight:
anglebisector:
Ch1.6DescribingPairsofAngles
Vocabulary
complementaryangles: supplementaryangles:
Angle Addition Postulate
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BigIdeasCh1Notes
adjacentangles:
Example1.Usingthediagramtotheright,nameapairofcomplementaryangles,supplementaryangles,andapairofadjacentangles.
2.Assume_________isacomplementof_________,and______________,Determine___________.
3.Assume_________isasupplementof_________,and________________,Determine_________.
Vocabulary
linearpair: verBcalangles:
Example1.Namethever>calangles
2.Namethelinearpairs
InterpreBngaDiagramUsingthediagramtotheright.
Wecanassume:
Wecannotassume:
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