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Parallel Lines

Skew Lines

Parallel Planes

If two parallel planes are cut by a th…

COPLANAR lines that do not intersect

NON coplanar lines that to not intersect (think left/right an…

Planes that do not intersect (Think floor and ceiling)

If planes X and Y are parallel, then their lines of intersect…

Parallel Lines

COPLANAR lines that do not intersect

Skew Lines

NON coplanar lines that to not intersect (think left/right an…

Betweenness of points theorem

Betweenness of rays theorem

Complements of the same angle

Supplements of the same angle

A-B-C, then AB+BC=AC

OA-OB-OC, then <AOB+<BOC=<AOC

are equal

are equal

Betweenness of points theorem

A-B-C, then AB+BC=AC

Betweenness of rays theorem

OA-OB-OC, then <AOB+<BOC=<AOC

Line AB

collinear points

plane

coplanar

2 or more points joined with no thickness or width that exten…

points that lie on the same line

flat 2 dimensional surface that extends indefinitely in all d…

objects that lie on the same plane

Line AB

2 or more points joined with no thickness or width that exten…

collinear points

points that lie on the same line

parallel lines

skew lines

parallel planes

transversal

two lines side by side that do not intersect or meet

noncoplanar and non-intersecting lines

two planes that do not intersect

a line that intersects two or more lines in a plane at differ…

parallel lines

two lines side by side that do not intersect or meet

skew lines

noncoplanar and non-intersecting lines

alternate exterior angles

alternate interior angles

corresponding angles

same side interior angles

nonadjacent exterior angles that lie on opposite sides of the…

nonadjacent interior angles that lie on opposite sides of the…

angles that lie on the same side of the transversal and in co…

interior angles that lie on the same side of the transversal

alternate exterior angles

nonadjacent exterior angles that lie on opposite sides of the…

alternate interior angles

nonadjacent interior angles that lie on opposite sides of the…

Parallel Lines

Skew Lines

Parallel Planes

Transversal Line

Coplanar lines that do not intersect.

Lines that do not intersect and are not coplanar.

Planes that do not intersect.

A line that intersects two or more coplanar lines at two diff…

Parallel Lines

Coplanar lines that do not intersect.

Skew Lines

Lines that do not intersect and are not coplanar.

parallel lines

skew lines

parallel planes

transversal

coplanar lines that do not intersect.

lines that do not intersect and are not coplanar

planes that do not intersect

a line that intersects two or more coplanar lines at two diff…

parallel lines

coplanar lines that do not intersect.

skew lines

lines that do not intersect and are not coplanar

point

line

plane

space

A location. It is a point with no length, width, and thickness.

infinite set of points that extends in two directions. It has…

infinite set of points that creates a flat surface that exten…

the set of all points

point

A location. It is a point with no length, width, and thickness.

line

infinite set of points that extends in two directions. It has…

Transversal

Alternate Interior Angles (AIA)

Same Side Interior Angles (SSIA)

Corresponding Angles (CA)

A line that intersects two or more lines.

Angles on opposite sides of the transversal in between the in…

Angles on the same side of the transversal in between the int…

In the same position around the transversal.

Transversal

A line that intersects two or more lines.

Alternate Interior Angles (AIA)

Angles on opposite sides of the transversal in between the in…

Parallel lines

Skew lines

Parallel planes

Parallel Postulate

Coplanar lines that do not intersect

Lines that do not intersect and are not coplanar

Two planes that do not intersect

If there is a line and a point not on the line, then there is…

Parallel lines

Coplanar lines that do not intersect

Skew lines

Lines that do not intersect and are not coplanar

angle bisector

perpendicular bisector

median

altitude

a ray that divides an angle into 2 congruent angles

a line/ray/segment that bisects a segment and is perpendicula…

a segment drawn from a vertex of a triangle to the midpoint o…

a segment drawn from a vertex of a triangle perpendicular to…

angle bisector

a ray that divides an angle into 2 congruent angles

perpendicular bisector

a line/ray/segment that bisects a segment and is perpendicula…

Parallel lines

Skew lines

Parallel planes

Transversal

coplanar lines that do not intersect

lines that do not intersect and are not coplanar

planes that do not intersect

a line that intersects two or more coplanar lines at two diff…

Parallel lines

coplanar lines that do not intersect

Skew lines

lines that do not intersect and are not coplanar

parallel lines

skew lines

parallel planes

parallel postulate

two lines if they do not intersect and are coplanar

two lines if they do not intersect and are not coplanar

two planes if they do not intersect

if there is a line and a point not on a line, then there is e…

parallel lines

two lines if they do not intersect and are coplanar

skew lines

two lines if they do not intersect and are not coplanar

Parallel

Skew

Transversal

Corresponding

Lines that do not intersect

Lines that do not intersect and are not coplanar

A line that intersect a set of parallel lines

A pair of angles that are in the "same spot" and do not touch…

Parallel

Lines that do not intersect

Skew

Lines that do not intersect and are not coplanar

CPCTC

angle bisector

perpendicular bisector

Median

Corresponding ... Parts of ... Congruent ... Triangle are... Congruent

a ray that divides an angle into 2 congruent angles- max 3

a ray or segment that bisects a segment into 2 congruent segm…

a segment drawn from a vertex of a triangle to the midpoint o…

CPCTC

Corresponding ... Parts of ... Congruent ... Triangle are... Congruent

angle bisector

a ray that divides an angle into 2 congruent angles- max 3

Segment Addition Postulate

Angle Addition Postulate

Addition Property

Subtraction Property

If B is a point on AC, then AB + BC = AC.

If point B lies in the interior of <AOC then m<AOB+ m<BOC = m…

If a = b, then a + c = b + c.

If a = b and c = d, then a - c = b - d.

Segment Addition Postulate

If B is a point on AC, then AB + BC = AC.

Angle Addition Postulate

If point B lies in the interior of <AOC then m<AOB+ m<BOC = m…

Parallel Lines

Skew Lines

Parallel Planes

Transversal

coplanar lines that do not intersect

lines that do not intersect and are not coplanar

planes that do not intersect

a line that intersects two or more coplanar lines at two diff…

Parallel Lines

coplanar lines that do not intersect

Skew Lines

lines that do not intersect and are not coplanar

Parallel lines

Parallel planes

Skew lines

Transversal

Coplanar lines that do not intersect

Planes that do not intersect

Lines that do not intersect and are not coplanar

A line that intersects 2 or more coplanar lines at two differ…

Parallel lines

Coplanar lines that do not intersect

Parallel planes

Planes that do not intersect

Undefined Terms

Carefully Defined

Postulates

Theorems

Such as point, line, plane

Most terms in a mathematical system are

Basic properties accepted without proofs

Other properties established by proofs

Undefined Terms

Such as point, line, plane

Carefully Defined

Most terms in a mathematical system are

parallel lines,

skew lines

parallel planes

transversal

they are coplanar and not do intersect

are not on the same plane, and do not intersect

two planes that do not intersect

a line that passes through two lines in the same plane on two…

parallel lines,

they are coplanar and not do intersect

skew lines

are not on the same plane, and do not intersect

parallel lines

parallel planes

skew lines

transversal

coplanar lines that do not intersect

planes that do not intersect

lines that do not intersect and are not coplanar

a line that intersects two or more lines in a plane at differ…

parallel lines

coplanar lines that do not intersect

parallel planes

planes that do not intersect

parallel lines

skew lines

transversal

alternate interior angles

coplanar lines that do not intersect

non coplanar lines ,they are neither parallel nor intersecting

a line that intersects two or more coplanar lines in differen…

two nonadjacent interior angles on opposite sides of the tran…

parallel lines

coplanar lines that do not intersect

skew lines

non coplanar lines ,they are neither parallel nor intersecting

Alternate Exterior Angles

Alternate Interior Angles

Corresponding angles

Distance From a Point to a Line

For two lines intersected by a transversal, a pair of angles…

For two lines intersected by a transversal, a pair of nonadja…

For two lines intersected by a transversal, a pair of angles…

The length of the perpendicular segment from the point to the…

Alternate Exterior Angles

For two lines intersected by a transversal, a pair of angles…

Alternate Interior Angles

For two lines intersected by a transversal, a pair of nonadja…

parallel lines

skew lines

parallel planes

transversal

coplanar lines that do not intersect

lines that do not intersect and are not coplanar

planes that do not instersect

a line that intersects two or more coplanar lines at two diff…

parallel lines

coplanar lines that do not intersect

skew lines

lines that do not intersect and are not coplanar

Parallel lines

Skew lines

Parallel planes

Postulate 13/14: Parallel/perpendicula…

Coplanar lines that do jot intersect

Non-Coplanar lines that do not intersect

Planes that do not intersect

If there is a line and a point not on that line, then there i…

Parallel lines

Coplanar lines that do jot intersect

Skew lines

Non-Coplanar lines that do not intersect

parallel lines

skew lines

parallel planes

transversal

are coplanar lines that do not intersect

are lines that do not intersect and are not coplanar

are planes that do not intersect

is a line that intersects two or more coplanar lines at two d…

parallel lines

are coplanar lines that do not intersect

skew lines

are lines that do not intersect and are not coplanar

alternate exterior angles

alternate interior angles

consecutive interior angles

corresponding angles

Angle 1 & angle 7, angle 2 & angle 8 are alternate exterior a…

Angle 4 & angle 6, angle 3 & angle 5 are alternate interior a…

one the same side a transversal; inside

positionaly the same

alternate exterior angles

Angle 1 & angle 7, angle 2 & angle 8 are alternate exterior a…

alternate interior angles

Angle 4 & angle 6, angle 3 & angle 5 are alternate interior a…

Parallel Lines

Skew Lines

Parallel Planes

Transversal

Coplanar lines that do not intersect

Lines that do not intersect and are NOT coplanar

Planes that do not intersect

A line that intersects two or more coplanar lines at two diff…

Parallel Lines

Coplanar lines that do not intersect

Skew Lines

Lines that do not intersect and are NOT coplanar

parallel lines

skew lines

parallel planes

a line parallel to a plane

two lines that are coplanar and never intersect

two lines that are non coplanar

two planes that never intersect

a line and a plane that never intersect

parallel lines

two lines that are coplanar and never intersect

skew lines

two lines that are non coplanar

Adjacent Angles

Linear Pair

Vertical Angles

Complementary Angles

Two angles that have no common vertex and a common side but n…

Two adjacent angles that are supplementary or form a straight…

Formed by intersecting lines and are across from one another.

Two angles whose sum is 90 degrees.

Adjacent Angles

Two angles that have no common vertex and a common side but n…

Linear Pair

Two adjacent angles that are supplementary or form a straight…

parallel lines

skew lines

parallel planes

transversal

coplanar lines that do not intersect.

lines that do not intersect and are not coplanar

planes that do not intersect

a line that intersects two or more coplanar lines at two diff…

parallel lines

coplanar lines that do not intersect.

skew lines

lines that do not intersect and are not coplanar

Axiom

Betweenness of points dfinition

Betweenness of Rays definition

Bisector of an angle

A self evident or aceept rule

A point is between two other points on the same line iff it's…

A ray is between two other Rays in the same hLf rotation iff…

A line bisects an angle iff it divides the angle into two equ…

Axiom

A self evident or aceept rule

Betweenness of points dfinition

A point is between two other points on the same line iff it's…

Betweenness of Points Theorem

Betweenness of Rays theorem

Complements of the same angle are ____…

Supplements of the same angle are ____…

A-B-C, then AB+BC=AC

OA-OB-OC, then <AOB+<BOC=<AOC

Complements of the same angle are equal.

Supplements of the same angle are equal.

Betweenness of Points Theorem

A-B-C, then AB+BC=AC

Betweenness of Rays theorem

OA-OB-OC, then <AOB+<BOC=<AOC

congruent angles

congruent figures

reflexive property

included angle

all pairs of corresponding parts are congruent

have the same shape and the same size

any segment or angles is congruent to itself

the angle formed by two sides of a triangle

congruent angles

all pairs of corresponding parts are congruent

congruent figures

have the same shape and the same size

Skew

Transversal

Corresponding angles

Alternate interior angles

No points in common, not in the same plane

A line which intersects two or more coplanar lines at differe…

Make an F shape

Make a Z shape, on opposite sides of the transversal and inne…

Skew

No points in common, not in the same plane

Transversal

A line which intersects two or more coplanar lines at differe…

Parallel Planes

Parallel Lines

Skew Lines

Transversal

Planes that do not intersect

Coplanar lines that don't intersect

Noncoplanar lines that don't intersect

A line that intersects two other lines

Parallel Planes

Planes that do not intersect

Parallel Lines

Coplanar lines that don't intersect

sketch

draw

construct

segment bisector

make freehand

use a protractor and ruler to be sure angles and sides are ex…

use compass and straight edge, do not erase

a line, ray, or segment that passes through the midpoint of t…

sketch

make freehand

draw

use a protractor and ruler to be sure angles and sides are ex…

parallel lines

skew lines

parallel planes

transversal

coplanar lines that don't intersect

noncoplanar; they aren't parallel and don't intersect

planes that don't intersect

a line that intersects two or more coplanar lines at distinct…

parallel lines

coplanar lines that don't intersect

skew lines

noncoplanar; they aren't parallel and don't intersect

Parallel lines

Skew lines

Parallel planes

Transversal

Two lines that do not intersect and are coplanar

Lines that do not intersect and are not coplanar

Two planes that do not intersect

A line that intersects two or more coplanar lines at differen…

Parallel lines

Two lines that do not intersect and are coplanar

Skew lines

Lines that do not intersect and are not coplanar

Same-side Interior Angle Postulate... If…

Alternate Interior Angles Theorem... If a…

Corresponding Angles Theorem... If a tran…

Alternate Exterior Angles Theorem... If a…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Same-side Interior Angle Postulate... If…

supplementary... m∠1 + m∠2 = 180

Alternate Interior Angles Theorem... If a…

congruent

Parallel Lines

Skew Lines

Parallel Planes

Transversal

coplanar lines that never intersect

lines that are not coplanar, not parallel, and don't intersect

planes that do not intersect

a line that intersects 2 or moe coplanar lines at distinct po…

Parallel Lines

coplanar lines that never intersect

Skew Lines

lines that are not coplanar, not parallel, and don't intersect

parallel lines

skew lines

parallel planes

parallel postulate

two lines if they do not intersect and are coplanar

two lines if they do not intersect and are not coplanar

two planes if they do not intersect

if there is a line and a point not on a line, then there is e…

parallel lines

two lines if they do not intersect and are coplanar

skew lines

two lines if they do not intersect and are not coplanar

Segment Addition Postulate

Angle Addition Postulate

Addition Property

Subtraction Property

If B is a point on AC, then AB + BC = AC.

If point B lies in the interior of <AOC then m<AOB+ m<BOC = m…

If a = b, then a + c = b + c.

If a = b and c = d, then a - c = b - d.

Segment Addition Postulate

If B is a point on AC, then AB + BC = AC.

Angle Addition Postulate

If point B lies in the interior of <AOC then m<AOB+ m<BOC = m…