Chapter 1 Basics of Geometry Ch 1.1 Points, Lines and Planesgreenstein.com/mvhs/geom/Lessons/Big Ideas Ch 1/Big Ideas Ch 1 N… · Chapter 1 Basics of Geometry Ch 1.1 Points, Lines

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( , )

BigIdeasCh1Notes

Ch1.4PerimeterandAreaintheCoordinatePlane

Proper>esofaPolygon:

ConvexPolygon: ConcavePolygon:

Classifythesepolygonsbytypeandconvexorconcave:1) 2) 3) 4)

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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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