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1.2UsingSegmentsandCongruenceNotes
1
1.2UseSegmentsandCongruence
Postulate/Axiom:ArulethatisACCEPTEDWITHOUTproof
Theorem:ArulethatCANBEprovedusingdefinitions,postulates,axioms,corollariesandothertheorem.
RulerPostulatePointsonalinecanbematchedonetoonewiththerealnumbers
calledcoordinates.
AlwaysPositive.Distancebetweentwopoints:
#1
SUN
#2
RAY
Whatisthedifferenceinthesetwopictures? SegmentAdditionPostulate
IfBisbetweenAandC,thenAB+BC=AC
segmentswithequallength.Congruentsegments:
Thelengthofisequaltothelengthof
iscongruentto
OR
1.2UsingSegmentsandCongruenceNotes
2
Segmentadditionpostulate:BisbetweenAC.AB=2AC=7FindBC=
BisbetweenACAC=23AB=x+1BC=3x2x=BC=
x=6BC=16answer
Ex2
Midpoint:Pointwhichdividesasegmentinto2congruentparts.
CisthemidpointofAB.AC=3x+5CB=2x+13x=AB=
x=8AB=58
Ex3
answer
BisthemidpointofAC.AB=4x1AC=10x20x=AB=
x=9AB=35
Ex4 cancreateatwocolumnproofasyousolve
answer
BisTHEMIDPOINTOFAC.AB=x+3CB=x+5AC=2x+2x=BC=
Ex5
x=18BC=23answer
BoardworkSegmentAdditionandMidpointWorksheet.docx
Youtryandwewillshareasajigsawinclass.
1.OisbetweensegmentDG
DO=3xOG=4x+1DG=36x=____OG=_____
2.AisthemidpointofsegmentJC
JA=5x+3AC=3x+11x=_____JC=_____
3.OisthemidpointofsegmentBY
BO=3x+16BY=14x4x=_____BY=______
4.AisthemidpointofsegmentCT
CA=x+2AT=3x+5CT=7x8x=____CT=____
Attachments
SegmentAdditionandMidpointWorksheet.docx
GeometryName: ____________________________
Segment Addition & Midpoints
1.
is between and
2.
is the midpoint of
3.
is between and
4.
is the midpoint of
5.
is the midpoint of
6.
is between and
7.
is the midpoint of
8.
is between and
9.
is the midpoint of
10.
is the midpoint of
D
:
29
35
Given
LD
EDx
LEx
=
=
=+
:
_____
_____
Find
x
LE
=
=
ZP
:
217
63
Given
EPx
ZEx
=+
=-
:
_____
_____
_____
Find
x
ZE
ZP
=
=
=
L
F
Y
:
126
15
927
Given
FLx
LY
FYx
=-
=
=+
:
_____
_____
_____
Find
x
FL
FY
=
=
=
R
ES
:
87
914
Given
ERx
ESx
=-
=+
:
_____
_____
_____
_____
Find
x
ER
RS
ES
=
=
=
=
A
VL
:
35
22
711
Given
ALx
VLx
=+
=-
:
_____
_____
_____
Find
x
AL
VA
=
=
=
E
D
H
:
2
3
3
22
5
Given
DEx
DHx
EHx
=+
=+
=+
:
_____
_____
_____
Find
x
DE
DH
=
=
=
B
AC
:
26
3
5
4
Given
ACx
BCx
=+
=+
:
_____
_____
_____
Find
x
BC
AC
=
=
=
C
E
B
D
:
43
813
62
Given
BCx
BDx
CDx
=+
=+
=+
:
_____
_____
_____
_____
Find
x
BC
CD
BD
=
=
=
=
B
AC
:
5
6
2
912
Given
ABx
ACx
=+
=-
:
_____
_____
_____
Find
x
AC
BC
=
=
=
C
AB
L
:
33
51
Given
ACx
CBx
=+
=-
:
_____
_____
_____
Find
x
AC
AB
=
=
=
SMART Notebook
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