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1
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UNIT1
Basicsof
Geometry
Aug109:04PM
BuildingBlocksofGeometryA) Point
alocationinspace1) hasnosize2) NamedbyONEcapitalletter
B) Spacethesetofallpoints
C) Lineextendsinoppositedirectionswithoutend
1) hasnowidth2)
cannotbemeasured3)namedbyTWOcapitallettersorONElowercase
cursiveletter
A
GC l
1.1
Aug109:35PM
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2
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D) CollinearPointsarepointsthatlieonthesameline
P
I
O
N
T
a) Anytwopointsarecollinear!!
l
mR
b)Nameeachlinetwoways
Aug109:49PM
E)Planeaflatsurfacewithnothickness1)
extendsinalldirectionswithout
end2)namedbyONEcursivecapital
letteror3noncollinearpoints
B
WM
H
3)Nametheplanetwoways
Aug109:35PM
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3
Aug1011:27AM
F)Segmentpartofalinewithtwoendpoints.
C
G
CGrepresentsthemeasureofthesegment
CGrepresentsthepictureofthesegment
Aug109:42PM
G) Pointsandlinesinthesameplanearecoplanar.
a) Anythreepointsarecoplanar!!
B C
A D
F
E H
G
b)nameaplanethatcontainssegmentFG?
c)NametheplanesthatcontainD?
Aug1011:30AM
H) Raypartofalinewithoneendpoint*alwayslisttheendpointfirst*
vz
I) OppositeRaystwocollinearrayswithacommon
endpoint*alwaysformsaline*
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4
Aug158:00PM
III. PlanePostulatesA)
Postulate(oraxiom)isanacceptedstatementoffact.
1) Twopointsdeterminealine.
LP
I
2) Twoplanesintersectinexactlyoneline.
3) Threenoncollinearpointsdetermineexactlyoneplane.
B
WM
H
NB
M
GC
M
Jan249:59AM
Jan248:46AM
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5
Jan2410:00AM
Jan247:25AM
Jan232:49PM
Congruentsegmentsaresegmentsthathavethesamelength.
Inthediagram,PQ=RS,soyoucanwritePQRS.
Definition:
=~ means
1.2
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Aug158:27PM
C) Distancebetweentwopoints
1)onthenumberlineD=labl
Jan2312:52PM
Aug1510:00PM
D) SegmentAdditionPostulate(SAP)IfthreepointsA,B,andCare
collinearandBisbetweenAandC,then
A B CAB+BC=AC
Examples:1. IfBisbetweenAandC
AC=23AB=2x6BC=x7FindABandBC
2. IfNisbetweenAandBAN=4x20AB=x+40NB=2x+30FindAB
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7
Jan232:51PM
Aug1510:10PM
Jan232:54PM
Definition:
ThemidpointMofABisthepointthatbisects,ordivides,thesegmentintotwocongruentsegments.
IfMisthemidpointofAB,thenAM=MB.
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8
Jan232:53PM
Jan232:55PM
Examples:IfCisthemidpointofAB:
4. AC=5x+9CB=8x36FindAC
5. BC=2x+5AB=3x+18FindAB
Jan232:57PM
SegmentBisectorsegmentthatintersectsatthemidpointofasegment
PerpendicularBisectorisaline,segmentorraythatformsarightangleatitsmidpoint.
Definitions:
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Aug159:02PM
AngleRelationshipsA) Angle
formedbytworayswiththesameendpoint
B) AcuteAnglemeasures>0and90and
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10
Jan233:02PM
Aug1510:39PM
A O C
B
Examples:1. IfptBisinthe
interiorof
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Aug159:19PM
1.4ComplementaryAngles
twoangleswhosemeasureshaveasumof90
SupplementaryAnglestwoangleswhosemeasureshaveasumof180
AdjacentAnglestwocoplanarangleswithacommonside,commonvertex
12
Jan233:10PM
Aug159:24PM
LinearPairapairofanglesthatareadjacentandsupplementary
VerticalAnglestwononadjacentanglesformedbyintersectinglines
A
B
GN
LV
M E
O
(theyformaline)
*Allverticalanglesarecongruent*
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12
Jan233:08PM
Aug159:40PM
65o
3
21
Findthemeasureofeach:
m
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Aug1012:12PM
1.5UsingformulasinGeometry
4.Square A=s2
Aug1012:16PM
Examples:Findtheareaofeach.
1. 2.
10.5m
12m
8m
30cm
13cm31cm
3. x+1
x4.
Jan233:14PM
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14
Aug1012:20PM
Aug1012:22PM
8in
Jan233:15PM
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15
Aug2912:52PM
1.6A)Midpointonanumberline(averagetheendpoints)
(a+b)/2XisthemidpointofRandSR=5,S=9X=____
R=8,X=3S=____
Jan233:17PM
Jan233:19PM
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Aug268:12AM
Ex:IfMisthemidpointofthesegmentAB,
1) FindMif 2) FIndMif 3) FIndBifA(8,9) A(3,5) A(1,4)B(6,3)
B(2,7) M(1,5)
midpoint=_____________________
Jun1210:06PM
Ex: FindABifyouaregiventhefollowingpoints:
1) A(4,8)andB(2,3) 2) A(1,2)andB(2,4)
onthecoordinateplane
C)DistanceFormula
Aug1011:51AM
Intherighttriangle,aandbarethelegsandcisthehypotenuse,thena2+b2=c2
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Aug1011:52AM
Ex:1) 2) 3) leg=9cm
leg=_______hypotenuse=15cm2"
x
3"
9m
6m
x
Hint:Checkyourmeasures...thehypotenuseshouldbethelongest.
Aug1011:53AM
A
B
FindthedistanceofAB.
Aug1012:02PM
1.7TransformationsA. Transformation:theoperationthatmaps
(ormoves) thepreimageontotheimage.1.
Preimage:theoriginalfigure(ptA)2.
Image:theresultingfigure(ptA')
A A'(A maps to A')
B. Fourbasictransformations1. Reflection2. Rotation3.
Translation4. Dilation
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Aug1012:04PM
TranslationsC. Translation:anisometrythat
mapsall pointsofafigurethesamedistanceinthe samedirection.SLIDE
FrogA
FrogB
Aug1012:05PM
Coordinatenotation:usedtodescribea
translationinacoordinateplane.
(x,y)(x+a,y+b)
Jan233:24PM
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Jan233:26PM
Jan233:26PM
Jan233:27PM
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Jan233:27PM
Aug1012:09PM
III. ReflectionsA. Reflection:atransformation
usingalinethatactslikeamirror.
B. LineofReflection:themirrorline.
Sep116:56AM
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Feb33:10PM
_____ptsdeterminealine_____ptsdetermineaplane
R postulateR theorem
r
AR
AR
AR
80 1
Why?802
Why?m
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Aug158:21PM
CP:pg29 #116pg32 #7073pg47 #819
HOMEWORK
Aug1511:02PM
VI. PatternsandReasoningA) InductiveReasoning
reasoningbasedonpatternsyouobserveB) Conjecture
educatedguessMakeaconjecture:1.
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Aug298:57AM
D)
DeductiveReasoningprocessoffacts,definitions,acceptedpropertiesinalogicalorder
Ex:Giveanexampleofdeductivereasoning
Aug299:11AM
Pythagorasandhisstudentsbelievedthateverythingwasrelatedtomathematicsandthatnumbersweretheultimatereality,and,throughmathematics,everythingcouldbepredictedandmeasuredinrhythmicpatternsorcycles.
WhattypeofreasoningdidPythagorasprobablyuse?
Aug158:21PM
CP:pg7 #2931#3437
pg538 #715(odd)#1924
HOMEWORK
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24
Aug158:57PM
D) Parallellinescoplanarlinesthatneverintersect
E) SkewLinesnoncoplanarlinesthatneverintersect
A
B C
D
E
F
H
G
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Attachments
UNIT1PP.ppt
UNIT 1
Tools
for
Geometry
I. Patterns and Reasoning
A.Inductive Reasoning: reasoning based on patterns you
observe.
B. Conjecture: a conclusion reached using inductive reasoning
(educated guess)
C. Counterexample: an example that makes a conjecture false.
Building Blocks
of Geometry
A. Space: set of all points
B. Point: location in space
1. has no size
2. all geometric figures are made of points.
SMART Notebook
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