Points that lie on the same line. Collinear points.
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Transcript of Points that lie on the same line. Collinear points.
![Page 1: Points that lie on the same line. Collinear points.](https://reader035.fdocuments.net/reader035/viewer/2022062300/56649f445503460f94c652f3/html5/thumbnails/1.jpg)
Points that lie on the Points that lie on the same line same line
Points that lie on the Points that lie on the same line same line
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Collinear pointsCollinear pointsCollinear pointsCollinear points
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points that don't lie points that don't lie on the same lineon the same line
points that don't lie points that don't lie on the same lineon the same line
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Non-collinear pointsNon-collinear pointsNon-collinear pointsNon-collinear points
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objects which lie on objects which lie on the same planethe same plane
objects which lie on objects which lie on the same planethe same plane
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Coplanar objectsCoplanar objectsCoplanar objectsCoplanar objects
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objects which don't objects which don't lie on the same planelie on the same planeobjects which don't objects which don't
lie on the same planelie on the same plane
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Non-coplanar objectsNon-coplanar objectsNon-coplanar objectsNon-coplanar objects
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statement that we statement that we accept without proofaccept without proofstatement that we statement that we
accept without proofaccept without proof
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PostulatePostulatePostulatePostulate
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statement that we statement that we can prove using logiccan prove using logicstatement that we statement that we
can prove using logiccan prove using logic
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TheoremTheoremTheoremTheorem
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the intersection of the intersection of two linestwo lines
the intersection of the intersection of two linestwo lines
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PointPointPointPoint
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the intersection of the intersection of two planestwo planes
the intersection of the intersection of two planestwo planes
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LineLineLineLine
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two coplanar lines two coplanar lines that don't intersectthat don't intersecttwo coplanar lines two coplanar lines that don't intersectthat don't intersect
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Parallel linesParallel linesParallel linesParallel lines
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two points and all two points and all points between thempoints between them
two points and all two points and all points between thempoints between them
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SegmentSegmentSegmentSegment
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segments with equal segments with equal lengthslengths
segments with equal segments with equal lengthslengths
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Congruent segmentsCongruent segmentsCongruent segmentsCongruent segments
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point that divides a point that divides a segment into two segment into two
congruent segmentscongruent segments
point that divides a point that divides a segment into two segment into two
congruent segmentscongruent segments
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MidpointMidpointMidpointMidpoint
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object that divides a object that divides a segment into two segment into two
congruent segmentscongruent segments
object that divides a object that divides a segment into two segment into two
congruent segmentscongruent segments
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Segment bisectorSegment bisectorSegment bisectorSegment bisector
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a part of a line that a part of a line that has only one has only one
endpointendpoint
a part of a line that a part of a line that has only one has only one
endpointendpoint
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RayRayRayRay
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rays with the same rays with the same endpoint which endpoint which
together form a linetogether form a line
rays with the same rays with the same endpoint which endpoint which
together form a linetogether form a line
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Opposite raysOpposite raysOpposite raysOpposite rays
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two rays joined by a two rays joined by a common endpointcommon endpoint
two rays joined by a two rays joined by a common endpointcommon endpoint
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AngleAngleAngleAngle
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common endpoint of common endpoint of two rays that form an two rays that form an
angleangle
common endpoint of common endpoint of two rays that form an two rays that form an
angleangle
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VertexVertexVertexVertex
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angle with measure angle with measure less than 90 degreesless than 90 degreesangle with measure angle with measure less than 90 degreesless than 90 degrees
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Acute angleAcute angleAcute angleAcute angle
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angle with measure angle with measure exactly 90 degreesexactly 90 degreesangle with measure angle with measure exactly 90 degreesexactly 90 degrees
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Right angleRight angleRight angleRight angle
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angle with measure angle with measure between 90 degrees between 90 degrees
and 180 degreesand 180 degrees
angle with measure angle with measure between 90 degrees between 90 degrees
and 180 degreesand 180 degrees
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Obtuse angleObtuse angleObtuse angleObtuse angle
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angle with measure angle with measure exactly 180 degreesexactly 180 degreesangle with measure angle with measure exactly 180 degreesexactly 180 degrees
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Straight angleStraight angleStraight angleStraight angle
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object (such as a ray or object (such as a ray or line) which divides an line) which divides an
angle into two angle into two congruent anglescongruent angles
object (such as a ray or object (such as a ray or line) which divides an line) which divides an
angle into two angle into two congruent anglescongruent angles
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Angle bisectorAngle bisectorAngle bisectorAngle bisector
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a unit to measure a unit to measure angles which equals a angles which equals a fraction (1/360th) of a fraction (1/360th) of a
circlecircle
a unit to measure a unit to measure angles which equals a angles which equals a fraction (1/360th) of a fraction (1/360th) of a
circlecircle
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DegreeDegreeDegreeDegree
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the number of the number of degrees in one-fourth degrees in one-fourth
of a circleof a circle
the number of the number of degrees in one-fourth degrees in one-fourth
of a circleof a circle
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90909090
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the number of the number of degrees in one-half of degrees in one-half of
a circlea circle
the number of the number of degrees in one-half of degrees in one-half of
a circlea circle
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180180180180
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the number of the number of degrees in a circledegrees in a circle
the number of the number of degrees in a circledegrees in a circle
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360360360360
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angles whose angles whose measures are equalmeasures are equal
angles whose angles whose measures are equalmeasures are equal
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Congruent anglesCongruent anglesCongruent anglesCongruent angles
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coplanar angles with a coplanar angles with a common vertex and common vertex and side, but no common side, but no common
interior pointsinterior points
coplanar angles with a coplanar angles with a common vertex and common vertex and side, but no common side, but no common
interior pointsinterior points
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Adjacent anglesAdjacent anglesAdjacent anglesAdjacent angles
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a pair of angles a pair of angles whose measures add whose measures add
to 90 degreesto 90 degrees
a pair of angles a pair of angles whose measures add whose measures add
to 90 degreesto 90 degrees
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Complementary anglesComplementary anglesComplementary anglesComplementary angles
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a pair of angles a pair of angles whose measures add whose measures add
to 180 degreesto 180 degrees
a pair of angles a pair of angles whose measures add whose measures add
to 180 degreesto 180 degrees
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Supplementary anglesSupplementary anglesSupplementary anglesSupplementary angles
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a pair of a pair of supplementary and supplementary and
adjacent anglesadjacent angles
a pair of a pair of supplementary and supplementary and
adjacent anglesadjacent angles
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Linear pairLinear pairLinear pairLinear pair
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a pair of “opposite” a pair of “opposite” angles formed by a angles formed by a pair of intersecting pair of intersecting
lineslines
a pair of “opposite” a pair of “opposite” angles formed by a angles formed by a pair of intersecting pair of intersecting
lineslines
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Vertical anglesVertical anglesVertical anglesVertical angles
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a statement that can a statement that can be written in the be written in the
form, "if p, then q.“form, "if p, then q.“
a statement that can a statement that can be written in the be written in the
form, "if p, then q.“form, "if p, then q.“
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Conditional Conditional statement statement Conditional Conditional statement statement
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the given information: the given information: part of a conditional part of a conditional
statement found statement found immediately after the immediately after the
word ifword if
the given information: the given information: part of a conditional part of a conditional
statement found statement found immediately after the immediately after the
word ifword if
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HypothesisHypothesisHypothesisHypothesis
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the result of the the result of the hypothesis: part of a hypothesis: part of a
conditional statement conditional statement found immediately after found immediately after
the word thenthe word then
the result of the the result of the hypothesis: part of a hypothesis: part of a
conditional statement conditional statement found immediately after found immediately after
the word thenthe word then
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ConclusionConclusionConclusionConclusion
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example showing a example showing a statement is not statement is not
ALWAYS true, and is ALWAYS true, and is therefore falsetherefore false
example showing a example showing a statement is not statement is not
ALWAYS true, and is ALWAYS true, and is therefore falsetherefore false
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CounterexampleCounterexampleCounterexampleCounterexample
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statement obtained statement obtained from a conditional from a conditional
statement by switching statement by switching the hypothesis and the the hypothesis and the
conclusionconclusion
statement obtained statement obtained from a conditional from a conditional
statement by switching statement by switching the hypothesis and the the hypothesis and the
conclusionconclusion
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ConverseConverseConverseConverse
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statement obtained statement obtained from a conditional from a conditional
statement by negating statement by negating the hypothesis and the the hypothesis and the
conclusionconclusion
statement obtained statement obtained from a conditional from a conditional
statement by negating statement by negating the hypothesis and the the hypothesis and the
conclusionconclusion
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InverseInverseInverseInverse
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statement obtained statement obtained from a conditional from a conditional
statement by negating statement by negating AND switching the AND switching the
hypothesis and hypothesis and conclusionconclusion
statement obtained statement obtained from a conditional from a conditional
statement by negating statement by negating AND switching the AND switching the
hypothesis and hypothesis and conclusionconclusion
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ContrapositiveContrapositiveContrapositiveContrapositive
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statement combining a statement combining a conditional statement conditional statement with its converse using with its converse using the phrase "if and only the phrase "if and only
if“if“
statement combining a statement combining a conditional statement conditional statement with its converse using with its converse using the phrase "if and only the phrase "if and only
if“if“
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Biconditional statementBiconditional statementBiconditional statementBiconditional statementMYP and PSC onlyMYP and PSC only
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a diagram with two or a diagram with two or more overlapping more overlapping
circles, used to show circles, used to show relationships between relationships between
sets. sets.
a diagram with two or a diagram with two or more overlapping more overlapping
circles, used to show circles, used to show relationships between relationships between
sets. sets.
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Venn DiagramVenn DiagramVenn DiagramVenn Diagram
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If p --> q is a true If p --> q is a true conditional and p is conditional and p is true, then q is true. true, then q is true.
If p --> q is a true If p --> q is a true conditional and p is conditional and p is true, then q is true. true, then q is true.
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Law of DetachmentLaw of DetachmentLaw of DetachmentLaw of Detachment
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If p --> q and q --> r If p --> q and q --> r are true conditionals, are true conditionals, then p --> r is true.then p --> r is true.
If p --> q and q --> r If p --> q and q --> r are true conditionals, are true conditionals, then p --> r is true.then p --> r is true.
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Law of SyllogismLaw of SyllogismLaw of SyllogismLaw of Syllogism
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lines that have a lines that have a point in commonpoint in commonlines that have a lines that have a point in commonpoint in common
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Intersecting linesIntersecting linesIntersecting linesIntersecting lines
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coplanar lines that do coplanar lines that do not intersect.not intersect.
coplanar lines that do coplanar lines that do not intersect.not intersect.
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Parallel linesParallel linesParallel linesParallel lines
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lines that intersect at lines that intersect at right anglesright angles
lines that intersect at lines that intersect at right anglesright angles
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Perpendicular linesPerpendicular linesPerpendicular linesPerpendicular lines
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lines that are non-lines that are non-coplanar and do not coplanar and do not
intersectintersect
lines that are non-lines that are non-coplanar and do not coplanar and do not
intersectintersect
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Skew linesSkew linesSkew linesSkew lines
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lines that intersect lines that intersect but are not but are not
perpendicularperpendicular
lines that intersect lines that intersect but are not but are not
perpendicularperpendicular
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Oblique linesOblique linesOblique linesOblique lines
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The steepness of a line The steepness of a line expressed as a ratio, expressed as a ratio,
using any two points on using any two points on the linethe line
The steepness of a line The steepness of a line expressed as a ratio, expressed as a ratio,
using any two points on using any two points on the linethe line
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SlopeSlopeSlopeSlope
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a line that intersects a line that intersects two other lines, at two other lines, at
different pointsdifferent points
a line that intersects a line that intersects two other lines, at two other lines, at
different pointsdifferent points
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TransversalTransversalTransversalTransversal
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a pair of angles, both in a pair of angles, both in the same position the same position
relative to two lines relative to two lines crossed by a transversal crossed by a transversal
(that is, upper right, (that is, upper right, etc)etc)
a pair of angles, both in a pair of angles, both in the same position the same position
relative to two lines relative to two lines crossed by a transversal crossed by a transversal
(that is, upper right, (that is, upper right, etc)etc)
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Corresponding anglesCorresponding anglesCorresponding anglesCorresponding angles
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One pair of corresponding angles is
2 and ___
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4444
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a pair of angles, both a pair of angles, both between two parallel between two parallel lines and on opposite lines and on opposite
sides of the transversalsides of the transversal
a pair of angles, both a pair of angles, both between two parallel between two parallel lines and on opposite lines and on opposite
sides of the transversalsides of the transversal
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Alternate interior Alternate interior anglesangles
Alternate interior Alternate interior anglesangles
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One pair of alternate interior angles is
2 and ___
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6666
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a pair of angles, both a pair of angles, both exterior to two parallel exterior to two parallel lines and on opposite lines and on opposite
sides of the transversalsides of the transversal
a pair of angles, both a pair of angles, both exterior to two parallel exterior to two parallel lines and on opposite lines and on opposite
sides of the transversalsides of the transversal
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Alternate exterior Alternate exterior anglesangles
Alternate exterior Alternate exterior anglesangles
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One pair of alternate exterior angles is
1 and ___
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a pair of angles, both a pair of angles, both between two parallel between two parallel lines and on the same lines and on the same side of the transversalside of the transversal
a pair of angles, both a pair of angles, both between two parallel between two parallel lines and on the same lines and on the same side of the transversalside of the transversal
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Consecutive interior Consecutive interior lineslines
Consecutive interior Consecutive interior lineslines
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One pair of consecutive interior angles is
2 and ___
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3333
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a pair of angles, both a pair of angles, both exterior to two parallel exterior to two parallel lines and on the same lines and on the same side of the transversalside of the transversal
a pair of angles, both a pair of angles, both exterior to two parallel exterior to two parallel lines and on the same lines and on the same side of the transversalside of the transversal
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Consecutive exterior Consecutive exterior anglesangles
Consecutive exterior Consecutive exterior anglesangles
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One pair of consecutive exterior angles is
8 and ___
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