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

Collinear pointsCollinear pointsCollinear pointsCollinear points

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

Non-collinear pointsNon-collinear pointsNon-collinear pointsNon-collinear points

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

Coplanar objectsCoplanar objectsCoplanar objectsCoplanar objects

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

Non-coplanar objectsNon-coplanar objectsNon-coplanar objectsNon-coplanar objects

statement that we statement that we accept without proofaccept without proofstatement that we statement that we

accept without proofaccept without proof

PostulatePostulatePostulatePostulate

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

TheoremTheoremTheoremTheorem

the intersection of the intersection of two linestwo lines

the intersection of the intersection of two linestwo lines

PointPointPointPoint

the intersection of the intersection of two planestwo planes

the intersection of the intersection of two planestwo planes

LineLineLineLine

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

Parallel linesParallel linesParallel linesParallel lines

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

SegmentSegmentSegmentSegment

segments with equal segments with equal lengthslengths

segments with equal segments with equal lengthslengths

Congruent segmentsCongruent segmentsCongruent segmentsCongruent segments

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

MidpointMidpointMidpointMidpoint

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

Segment bisectorSegment bisectorSegment bisectorSegment bisector

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

RayRayRayRay

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

Opposite raysOpposite raysOpposite raysOpposite rays

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

AngleAngleAngleAngle

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

VertexVertexVertexVertex

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

Acute angleAcute angleAcute angleAcute angle

angle with measure angle with measure exactly 90 degreesexactly 90 degreesangle with measure angle with measure exactly 90 degreesexactly 90 degrees

Right angleRight angleRight angleRight angle

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

Obtuse angleObtuse angleObtuse angleObtuse angle

angle with measure angle with measure exactly 180 degreesexactly 180 degreesangle with measure angle with measure exactly 180 degreesexactly 180 degrees

Straight angleStraight angleStraight angleStraight angle

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

Angle bisectorAngle bisectorAngle bisectorAngle bisector

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

DegreeDegreeDegreeDegree

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

90909090

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

180180180180

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

360360360360

angles whose angles whose measures are equalmeasures are equal

angles whose angles whose measures are equalmeasures are equal

Congruent anglesCongruent anglesCongruent anglesCongruent angles

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

Adjacent anglesAdjacent anglesAdjacent anglesAdjacent angles

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

Complementary anglesComplementary anglesComplementary anglesComplementary angles

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

Supplementary anglesSupplementary anglesSupplementary anglesSupplementary angles

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

Linear pairLinear pairLinear pairLinear pair

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

Vertical anglesVertical anglesVertical anglesVertical angles

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.“

Conditional Conditional statement statement Conditional Conditional statement statement

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

HypothesisHypothesisHypothesisHypothesis

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

ConclusionConclusionConclusionConclusion

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

CounterexampleCounterexampleCounterexampleCounterexample

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

ConverseConverseConverseConverse

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

InverseInverseInverseInverse

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

ContrapositiveContrapositiveContrapositiveContrapositive

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“

Biconditional statementBiconditional statementBiconditional statementBiconditional statementMYP and PSC onlyMYP and PSC only

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.

Venn DiagramVenn DiagramVenn DiagramVenn Diagram

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.

Law of DetachmentLaw of DetachmentLaw of DetachmentLaw of Detachment

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.

Law of SyllogismLaw of SyllogismLaw of SyllogismLaw of Syllogism

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

Intersecting linesIntersecting linesIntersecting linesIntersecting lines

coplanar lines that do coplanar lines that do not intersect.not intersect.

coplanar lines that do coplanar lines that do not intersect.not intersect.

Parallel linesParallel linesParallel linesParallel lines

lines that intersect at lines that intersect at right anglesright angles

lines that intersect at lines that intersect at right anglesright angles

Perpendicular linesPerpendicular linesPerpendicular linesPerpendicular lines

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

Skew linesSkew linesSkew linesSkew lines

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

Oblique linesOblique linesOblique linesOblique lines

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

SlopeSlopeSlopeSlope

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

TransversalTransversalTransversalTransversal

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)

Corresponding anglesCorresponding anglesCorresponding anglesCorresponding angles

One pair of corresponding angles is

2 and ___

4444

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

Alternate interior Alternate interior anglesangles

Alternate interior Alternate interior anglesangles

One pair of alternate interior angles is

2 and ___

6666

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

Alternate exterior Alternate exterior anglesangles

Alternate exterior Alternate exterior anglesangles

One pair of alternate exterior angles is

1 and ___

5555

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

Consecutive interior Consecutive interior lineslines

Consecutive interior Consecutive interior lineslines

One pair of consecutive interior angles is

2 and ___

3333

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

Consecutive exterior Consecutive exterior anglesangles

Consecutive exterior Consecutive exterior anglesangles

One pair of consecutive exterior angles is

8 and ___

5555