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a line that intersects two or more cop…

Inside the parallel lines and on oppos…

lie on the same side of the transversa…

Angles that have the same relative pos…

Transversal

Alternate Interior Angles

Consecutive Interior Angles

Corresponding Angles

a line that intersects two or more cop…

Transversal

Inside the parallel lines and on oppos…

Alternate Interior Angles

transversal

alternate angles

corresponding

Corresponding Angle Postulate

a line that crosses over two parallel lines

two angles that are on opposite sides of the transversal (int…

refer to the position in the group of four angles

corresponding angles are congruent

transversal

a line that crosses over two parallel lines

alternate angles

two angles that are on opposite sides of the transversal (int…

Parallel Lines

Vertical angles

Supplementary angles

Transversal

Lines that never intersect.

angles formed when two lines intersect that across from one a…

angles whose sum is 180 degrees

a line that intersects 2 or more parallel lines

Parallel Lines

Lines that never intersect.

Vertical angles

angles formed when two lines intersect that across from one a…

Parallel Lines

Vertical angles

Supplementary angles

Transversal

Lines that never intersect.

angles formed when two lines intersect that across from one a…

angles whose sum is 180 degrees

a line that intersects 2 or more parallel lines

Parallel Lines

Lines that never intersect.

Vertical angles

angles formed when two lines intersect that across from one a…

corresponding angles

alternate interior angles

interior angles on the same side

vertical angles

If parallel lines are cut by a transversal, then correspondin…

If parallel lines are cut by a transversal,then alternate int…

If parallel lines are cut by a transversal, then interior ang…

Vertical angles are equal in measure

corresponding angles

If parallel lines are cut by a transversal, then correspondin…

alternate interior angles

If parallel lines are cut by a transversal,then alternate int…

parallel lines

skew

parallel plane

transversal

coplanar; never intersect

lines on separate planes that never intersect

two planes that never intersect (example: front and back of a…

line that intersects 2 or more coplanar lines

parallel lines

coplanar; never intersect

skew

lines on separate planes that never intersect

Corresponding Angles

Alternate Interior Angles

Alternate Exterior Angles

Same Side or Consecutive Interior Angles

Angles that are in the same relative position - they are cong…

Angles that are both inside the parallel lines and are on opp…

Angles that are both outside of the parallel lines and are on…

Angles that are both inside the parallel lines and are on the…

Corresponding Angles

Angles that are in the same relative position - they are cong…

Alternate Interior Angles

Angles that are both inside the parallel lines and are on opp…

parallel lines

skew

parallel plane

transversal

coplanar; never intersect

lines on separate planes that never intersect

two planes that never intersect (example: front and back of a…

line that intersects 2 or more coplanar lines

parallel lines

coplanar; never intersect

skew

lines on separate planes that never intersect

Parallel Lines

Skew Lines

Perpendicular Lines

Transversal

Coplanar lines that do not intersect - lines that are the sam…

Non-coplanar lines that do not intersect

Two lines that intersect to form a right angle

A line that intersects at least two other lines

Parallel Lines

Coplanar lines that do not intersect - lines that are the sam…

Skew Lines

Non-coplanar lines that do not intersect

Corresponding Angles

Alternate Interior Angles

Alternate Exterior Angles

Same Side or Consecutive Interior Angles

Angles that are in the same relative position - they are cong…

Angles that are both inside the parallel lines and are on opp…

Angles that are both outside of the parallel lines and are on…

Angles that are both inside the parallel lines and are on the…

Corresponding Angles

Angles that are in the same relative position - they are cong…

Alternate Interior Angles

Angles that are both inside the parallel lines and are on opp…

Parallel Postulate

Congruent Linear Pair Theorem

Adjacent Acute Angles Theorem

Perpendicular Four Right Angle Theorem

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

If two lines intersect to form a linear pair of congruent ang…

If two sides of two adjacent angles are perpendicular, then t…

If two lines are perpendicular, then they intersect to form f…

Parallel Postulate

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

Congruent Linear Pair Theorem

If two lines intersect to form a linear pair of congruent ang…

Transversal

Alternate Interior Angles

Consecutive Interior Angles

Corresponding Angles

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

Inside the parallel lines and on opposite (alternate) sides o…

lie on the same side of the transversal and on the interior o…

Angles that have the same relative position

Transversal

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

Alternate Interior Angles

Inside the parallel lines and on opposite (alternate) sides o…

parallel lines

skew lines

postulate

postulate

coplanar lines that don't intersect [symbol is II]

non parallel lines

in a plane, two lines perpendicular to the same segment are p…

through a point not on a line, there is exactly one line para…

parallel lines

coplanar lines that don't intersect [symbol is II]

skew lines

non parallel lines

parallel lines

parallel planes

skew lines

transversals

lines in the same plane that never intersect

planes that do not intersect

Lines in three dimensional space that do not intersect and ar…

a line that intersects two or more lines at unique points

parallel lines

lines in the same plane that never intersect

parallel planes

planes that do not intersect

Parallell Lines

Alternate interior angles

Same side interior angles

Corresponding angles

Two or more lines that never touch

Angles that are opposite Angles that are transversals in betw…

Angles that are transversals on the same side in between para…

Angles that are either left and above or right and above

Parallell Lines

Two or more lines that never touch

Alternate interior angles

Angles that are opposite Angles that are transversals in betw…

parallel

Euclidean Geometry

Euclid's First Postulate

Euclid's Second Postulate

two lines which do not intersect

built from the foundation of five postulates, twenty-three de…

to a draw a straight line from any point to any point

to produce a finite straight line continuously in a straight…

parallel

two lines which do not intersect

Euclidean Geometry

built from the foundation of five postulates, twenty-three de…

Parallel Lines

Skew Lines

Perpendicular Lines

Transversal

Coplanar lines that do not intersect - lines that are the sam…

Non-coplanar lines that do not intersect

Two lines that intersect to form a right angle

A line that intersects at least two other lines

Parallel Lines

Coplanar lines that do not intersect - lines that are the sam…

Skew Lines

Non-coplanar lines that do not intersect

Definition of Parallel Lines

Symbol used to denote two parallel lines

Parallel Planes

Skew Line

Two lines on the same plane that do not intersect.

Two planes that do not intersect

Two lines that do not intersect AND are not on the same plan.

Definition of Parallel Lines

Two lines on the same plane that do not intersect.

Symbol used to denote two parallel lines

Corresponding Angles, Congruent

Same-Side Interior Angles, Supplementary

Alternate Exterior Angles, Congruent

Alternate Interior Angles, Congruent

What is the angle relationship? Is it congruent or supplement…

What is the angle relationship? Is it congruent or supplement…

What is the angle relationship? Is it congruent or supplement…

What is the angle relationship? Is it congruent or supplement…

Corresponding Angles, Congruent

What is the angle relationship? Is it congruent or supplement…

Same-Side Interior Angles, Supplementary

What is the angle relationship? Is it congruent or supplement…

If Parallel then Corresponding Angles…

If Parallel then Alternate Interior An…

If Parallel then Alternate Exterior An…

If Parallel then Consecutive Interior…

Postulate

Theorems

Theorems

Theorems

If Parallel then Corresponding Angles…

Postulate

If Parallel then Alternate Interior An…

Theorems

Corresponding Angles

Alternate Interior Angles

Alternate Exterior Angles

Same Side or Consecutive Interior Angles

Angles that are in the same relative position - they are cong…

Angles that are both inside the parallel lines and are on opp…

Angles that are both outside of the parallel lines and are on…

Angles that are both inside the parallel lines and are on the…

Corresponding Angles

Angles that are in the same relative position - they are cong…

Alternate Interior Angles

Angles that are both inside the parallel lines and are on opp…

parallel lines

skew lines

perpendicular lines

parallel planes

coplaner lines that never intersect

non-coplaner lines that do not intersect

2 lines that intersect at a 90 degree angle

planes that do not intersect

parallel lines

coplaner lines that never intersect

skew lines

non-coplaner lines that do not intersect

corresponding angle postulate

alternate interior angles theorum

alternate exterior angles theorum

consecutive interior angles theorum

if two parallel lines are cut by a transversal, then the pair…

if two parallel lines are cut by a transversal, then the pair…

if two parallel lines are cut by a transversal, then the pair…

if two parallel lines are cut by a transversal, then the pair…

corresponding angle postulate

if two parallel lines are cut by a transversal, then the pair…

alternate interior angles theorum

if two parallel lines are cut by a transversal, then the pair…

Transversal

Alternate Interior Angles

Corresponding Angles

Consecutive Interior Angles

line that crosses 2 coplanar lines at 2 different points

angles in the interior of a transversal that are on the same…

Transversal

line that crosses 2 coplanar lines at 2 different points

Alternate Interior Angles

parallel lines

perpendicular lines

parallel planes

line perpendicular to a plane

lines in the same plane that never intersect

Lines that intersect to form right angles

planes that do not intersect

a line that intersects the plane in a point and is perpendicu…

parallel lines

lines in the same plane that never intersect

perpendicular lines

Lines that intersect to form right angles

transversal

alternate angles

corresponding

Corresponding Angle Postulate

a line that crosses over two parallel lines

two angles that are on opposite sides of the transversal (int…

refer to the position in the group of four angles

corresponding angles are congruent

transversal

a line that crosses over two parallel lines

alternate angles

two angles that are on opposite sides of the transversal (int…

same side interior angles

alternate interior angles

corresponding angles

alternate exterior angles

lie on the same side of the transversal and between the inter…

non adjacent angles that lie on opposite sides of the transve…

lie on the same side of the transversal and on the same sides…

lie on opposite sides of the transversal and outside the inte…

same side interior angles

lie on the same side of the transversal and between the inter…

alternate interior angles

non adjacent angles that lie on opposite sides of the transve…

Parallel Lines

Skew lines

Transversal

Parallel Postulate

When two or more lines that do not intersect and are coplanar.

Lines that do not intersect an are not coplanar.

A line that intersects two or more lines in different points.

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

Parallel Lines

When two or more lines that do not intersect and are coplanar.

Skew lines

Lines that do not intersect an are not coplanar.

Transversal

Corresponding Angles

Alternate Angles

Interior Angles

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

two angles on the same side of the transversal, on a differen…

two angles formed by a transversal and the lines it crosses,…

two angles formed by a transversal and the lines it crosses,…

Transversal

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

Corresponding Angles

two angles on the same side of the transversal, on a differen…

corresponding angles postulate

alternate interior angles theorum

consecutive interior angles theorum

alternate exterior angles theorum

if two parallel lines are cut by a transversal, the each pair…

if two parallel lines are cut by a transversal, then each pai…

if two parallel lines are cut by a transversal, then each pai…

if two parallel line are cut by a transversal, then each pair…

corresponding angles postulate

if two parallel lines are cut by a transversal, the each pair…

alternate interior angles theorum

if two parallel lines are cut by a transversal, then each pai…

skew lines

transversal

interior angles

exterior

noncoplanar lines that never intersect

lines that intersect 2 or more lines

angles in between 2 lines cut by transversal

angles outside 2 lines cut by transversal

skew lines

noncoplanar lines that never intersect

transversal

lines that intersect 2 or more lines

Parallel

Transversal

Interior

Interior angles

•Two lines which do not intersect ... •A solid arrow placed on…

•A line,Ray or segment that intersects 2 or more coplanar lin…

•The space INSIDE the 2 lines

•The angles that lie in the area between the two parallel lin…

Parallel

•Two lines which do not intersect ... •A solid arrow placed on…

Transversal

•A line,Ray or segment that intersects 2 or more coplanar lin…

inductive reasoning

deductive reasoning

conjecture

counterexample

reasoning that is based on patterns you observe

(logical reasoning) the process of reasoning logically from g…

a conclusion that you reach using inductive reasoning

a conjecture is an example for which the conjecture is incorr…

inductive reasoning

reasoning that is based on patterns you observe

deductive reasoning

(logical reasoning) the process of reasoning logically from g…

Coplanar

Noncoplanar Lines

Interior Region

Exterior Region

lines, segments, rays, or points that lie on the same plane a…

also called skew lines; lines that lie on different planes.

the region bounded by both lines when a pair of lines are dra…

the outside area outside two lines when a pair of lines are d…

Coplanar

lines, segments, rays, or points that lie on the same plane a…

Noncoplanar Lines

also called skew lines; lines that lie on different planes.

Tranversal

Parallel Lines

Parallel Planes

Alternate Interior Angles

A line, ray, or line segment intersecting 2 other lines, rays…

2 lines that will not intersect

Ceiling and floor: 2 planes that do not intersect

Pair of angles on alternate sides of a tranversal, inside the…

Tranversal

A line, ray, or line segment intersecting 2 other lines, rays…

Parallel Lines

2 lines that will not intersect

Parallel lines

Parallel planes

Skew lines

Transversal

2 coplanar lines that do not interact; arrows are used to ind…

planes that do not intersect

non-coplanar lines that do not intersect

a line that intersects 2 or more lines

Parallel lines

2 coplanar lines that do not interact; arrows are used to ind…

Parallel planes

planes that do not intersect

transversal

corresponding angles

alternate interior angles

alternate exterior angles

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

Two angles that lie on the same side of the transversal and o…

Two nonadjacent angles that lie on opposite sides of the tran…

Two angles that lie on opposite sides of the transversal and…

transversal

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

corresponding angles

Two angles that lie on the same side of the transversal and o…

right angle

obtuse angle

straight angle

complementary angles

An angle that measures exactly 90 degrees.

An angle that is >90 degrees and <180 degrees.

An angle that measures exactly 180 degrees.

Angles whose measure adds up to 90 degrees.

right angle

An angle that measures exactly 90 degrees.

obtuse angle

An angle that is >90 degrees and <180 degrees.

Alternate Interior Angles

Alternate Exterior Angles

Consecutive Interior Angles (Same-Side…

Corresponding Angles

Angles on the inside of two lines and on opposite sides of a…

Angles on the outside of two lines and on opposite sides of t…

Angles on the inside of two lines and on the same side of the…

Angles in matching positions when a transversal crosses at le…

Alternate Interior Angles

Angles on the inside of two lines and on opposite sides of a…

Alternate Exterior Angles

Angles on the outside of two lines and on opposite sides of t…

coplanar

Skew Lines

Transversal

Perpendicular Bisector

On the same plane.

Lines in three dimensional space that do not intersect and ar…

A line that intersects two or more co-planar lines at differe…

A line, ray, segment, or plane that bisects a segment at a 90…

coplanar

On the same plane.

Skew Lines

Lines in three dimensional space that do not intersect and ar…

Parallel Lines

Skew Lines

Parallel Planes

Transversal

Coplanar lines that DO NOT intersect

non-coplanar; they are NOT parallel and DO NOT intersect

Planes that DO NOT intersect

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

Parallel Lines

Coplanar lines that DO NOT intersect

Skew Lines

non-coplanar; they are NOT parallel and DO NOT intersect

parallel

Skew

transversal

Exterior Angles

when lines in the same plane do not intersect

when lines are not in the same plane and do not intersect

a line that intersects 2 more lines in a plane at different p…

Angles on the outside of the transversal and the two lines it…

parallel

when lines in the same plane do not intersect

Skew

when lines are not in the same plane and do not intersect

transversal

corresponding angles

interior angles

exterior angles

a line that intersects two other lines at different points

the angles that occupy the same relative position at each int…

angles between parallel lines

angles outside parallel lines

transversal

a line that intersects two other lines at different points

corresponding angles

the angles that occupy the same relative position at each int…

plane

coplanar

noncoplanar

parallel lines

undefined term... flat surface that extends infinitely in all di…

on the same plane

not on the same plane

2 coplanar lines that do not intersect

plane

undefined term... flat surface that extends infinitely in all di…

coplanar

on the same plane

Transversal

How many angles does a transversal mak…

Corresponding angles

Alternate interior angles

Any line that intersects two or more lines in the same plane,…

8

The angles that appear to be in the same relative position in…

Angles that are wishing the lines being intersected, not adja…

Transversal

Any line that intersects two or more lines in the same plane,…

How many angles does a transversal mak…

8

If two lines are cut by a transversal…

AAS Congruence Theorem

HA Congruence Theorem

Angle Bisector Theorem

then the lines are parallel

If two angles and a side of one triangle are congruent respec…

If the hypotenuse and an acute angle of one right triangle ar…

A point P is on the bisector of an angle if and only if it is…

If two lines are cut by a transversal…

then the lines are parallel

AAS Congruence Theorem

If two angles and a side of one triangle are congruent respec…