definition of perpendicular lines (important): two lines that intersect to form right angles! a line...
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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
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
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.
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.
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
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.
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.
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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Reflexive Prop. Of equality
Symmetric Prop. Of equality
Transitive Prop. Of equality
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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
AA
ABAB
__________, thenBAIf
___________, thenCDABIf
___________, thenCBandBAIf
___________, thenEFCDandCDABIf
__________ Property
Symmetric Property
_________ Property
Right Angle Congruence Thrm - All ______ angles are _______
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 ________
Explain in your own words why congruent supplements theorem has to be true. This may show up on your test.
Vertical Angles Thrm - _____ angles are ______
Linear Pair Postulate – If two angles form a linear pair, then they are _________
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RAIm
WAIm
Find
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ary.complement are OAZ and IAO
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3m
2m
Find
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ary.supplement are 4 and 3
ary.supplement are 2 and 1
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pairlinare
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Prove 31 mm
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pairlinare
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anglespare
sup3,2
sup2,1
Def of Supp Angles
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PKMmJKNm
Given
Prove
75 mm
J 7
2.5-9 Number 2
V
Q
R
T
89
PQTmmm 98
Substitution Prop =
VQRmPQTm Given
Prove 108 mm
P 10