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Definition of Perpendicular lines (IMPORTANT): Two lines that
intersect to form RIGHT ANGLES!
A line perpendicular to a plane is a line that intersects
the plane in a point that is perpendicular to every line in
the plane that intersects it.symbollarperpendicuAll definitions work __________ and ___________
If two lines are perpendicular, then they form a ___________.
If two lines intersect to form ________________, then they are perpendicular.
2.2 – Definitions and Biconditional Statements
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All definitions work forwards and backwards
If two lines are perpendicular, then they form a right angle.
If two lines intersect to form right angles, then they are perpendicular.
If a conditional statement and its converse are both true, it is called biconditional, and you can combine them into a “if and
only if” statement
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True or false? Why? (Check some hw)Z Y
X
W V U
TS
R
WVZ and RVS form a linear pair.
YVU and TVR are supplementary
Y, V, and S are collinear
WVT and YVX are complementary.
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Write the conditional statement and the converse as a biconditional and see if
it’s true.If two segments are congruent, then their
lengths are the same.
If the lengths of the segments are the same, then they are congruent.
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Write the conditional statement and the converse as a biconditional and see if
it’s true.
If B is between A and C, then AB + BC = AC
If AB + BC = AC, then B is between A and C
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Write the converse of the statement, then write the biconditional statement. Then see if the biconditional statement is true or false. (Check more hw)
If x = 3, then x2 = 9
If two angles are a linear pair, then they are supplementary angles.
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Split up the biconditional into a conditional statement and its converse.
Pizza is healthy if and only if it has bacon.
Students are good citizens if and only if they follow the ESLRs.
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Warm – Up: Graph the following 4 equations.
y = 0 x = 0
y = x y = -x
2.4 – Reasoning with Properties from Algebra
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dbcathendcandbaIf ,
dbcathendcandbaIf ,
cbcathenbaIf ,
c
b
c
athencandbaIf ,0
)(
,
inequalityorequationanyin
otherthefordsubstitutebemay
boraeitherthenbaIf
aa
abthenbaIf ,
cathencbandbaIf ,
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Reasons
13125 x
Reasons
522
1x
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Reflexive Prop. Of equality
Symmetric Prop. Of equality
Transitive Prop. Of equality
DmDmDEDE
DmEmthenEmDmIf
DEFGthenFGDEIf
,
,
FmDmthen
FmEmandEmDmIf
JKDEthen
JKFGandFGDEIf
,
,
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We will fill in the blanks
M A T H AHMT:Prove
THMA:Given
THMA 1)
2)
3)
4)
5)
1)
2)
3)
4)
5)
Prop Reflexive
THATATMA
Post AddSegment
AHMT
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D
U C
K12
021m:Prove
50UDKm,302m:Given
50UDKm
,302m1)
2)
3)
4)
5)
1)
2)
3)
4)
5)
Post Add Angle
PropSubst
3030
021m
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A N G
SE LSAGroveP
LENGESANGiven
:
,:
L
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Copy a segment
1) Draw a line
2) Choose point on line
3) Set compass to original radius, transfer it to new line, draw an arc, label the intersection.
2.6 – Proving Statements about Angles
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AA
ABAB
__________, thenBAIf
___________, thenCDABIf
___________, thenCBandBAIf
___________, thenEFCDandCDABIf
__________ Property
Symmetric Property
_________ Property
Right Angle Congruence Thrm - All ______ angles are _______
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Congruent Supplements TheoremIf two angles are ____________ to the same angle (or to congruent angles), then they are congruent.
If _____ and _____ are supplementary and _____ and ____ are supplementarythen ________
Congruent Complements TheoremIf two angles are ____________ to the same angle (or to congruent angles), then they are congruent.
If _____ and _____ are complementary and _____ and ____ are complementarythen ________
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Explain in your own words why congruent supplements theorem has to be true. This may show up on your test.
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Vertical Angles Thrm - _____ angles are ______
Linear Pair Postulate – If two angles form a linear pair, then they are _________
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IASm
RALm
RAIm
WAIm
Find
35IAOm
ary.complement are OAZ and IAO
W
RI
O
ZS
A
L
4m
3m
2m
Find
551m
.3 2
ary.supplement are 4 and 3
ary.supplement are 2 and 1
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E
R A
T1 2
90ERAmGiven
Provearycomplement
areand 21
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12
3pairlinare
pairlinare
.3,2
.2,1
Given
Prove 31 mm
pairlinare
pairlinare
.3,2
.2,1
anglespare
anglespare
sup3,2
sup2,1
Def of Supp Angles
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P
K M
N5 6
JKNmmm 65
PKMmJKNm
Given
Prove
75 mm
J 7
2.5-9 Number 2
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V
Q
R
T
89
PQTmmm 98
Substitution Prop =
VQRmPQTm Given
Prove 108 mm
P 10