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Postulate 3-1 Same-side Interior Angle…

Theorem 3-1 Alternate Interior Angles…

Theorem 3-2 Corresponding Angles Theor…

Theorem 3-3 Alternate Exterior Angles…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Postulate 3-1 Same-side Interior Angle…

supplementary... m∠1 + m∠2 = 180

Theorem 3-1 Alternate Interior Angles…

congruent

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Theorem

Alternate Interior Angles Theorem

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

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

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

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

Parallel Postulate

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

Perpendicular Postulate

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

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Postulate

Alternate Interior Angles Theorem

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

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

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

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

Parallel Postulate

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

Perpendicular Postulate

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

Postulate 3-1 Same-side Interior Angle…

Theorem 3-1 Alternate Interior Angles…

Theorem 3-2 Corresponding Angles Theor…

Theorem 3-3 Alternate Exterior Angles…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Postulate 3-1 Same-side Interior Angle…

supplementary... m∠1 + m∠2 = 180

Theorem 3-1 Alternate Interior Angles…

congruent

Corresponding Angles Postulate - If tw…

Alternate Interior Angles Theorem - If…

Alternate Exterior Angles Theorem - If…

Same-Side Interior Angles Theorem - If…

then the pairs of corresponding angles are congruent.

then the alternate interior angles are congruent.

then the alternate exterior angles are congruent.

then the pairs of same-side interior angles are supplementary.

Corresponding Angles Postulate - If tw…

then the pairs of corresponding angles are congruent.

Alternate Interior Angles Theorem - If…

then the alternate interior angles are congruent.

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

Transversal

Alternate Interior Angles

Consecutive Interior Angles

Corresponding Angles

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

are inside the parallel lines, and on opposite (alternate) si…

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

are two nonadjacent angles that lie on the ... same side of the…

Transversal

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

Alternate Interior Angles

are inside the parallel lines, and on opposite (alternate) si…

Postulate 3-1: Same-Side Interior Angl…

Theorem 3-1: Alternate Interior Angles…

Theorem 3-2: Corresponding Angles Theo…

Theorem 3-3: Alternate Exterior Angles…

If at transversal intersects two parrallel lines, then same-s…

If a transversal intersects two parallel lines, then alternat…

If a transversal intersects two parallel lines, then correspo…

If a transversal intersects two parallel lines, then alternat…

Postulate 3-1: Same-Side Interior Angl…

If at transversal intersects two parrallel lines, then same-s…

Theorem 3-1: Alternate Interior Angles…

If a transversal intersects two parallel lines, then alternat…

Congruent linear pair theorem

Perpendicular transveral theorem

Perpendicular parallel theorem

Converse of corresponding angles postu…

If 2 intersecting lines form a linear pair of congruent angle…

In a plane, if a transversal is perpendicular to one of two p…

If two coplanar lines are perpendicular to the same line, the…

If corresponding angles are congruent, then parallel lines ar…

Congruent linear pair theorem

If 2 intersecting lines form a linear pair of congruent angle…

Perpendicular transveral theorem

In a plane, if a transversal is perpendicular to one of two p…

Postulate 3.1 Corresponding Angles Pos…

Theorem 3.1 Alternate Interior Angles…

Theorem 3.2 Consecutive Interior Angle…

Theorem 3.3 Exterior Angles Theorem

If two parallel lines are cut be a transversal, then each pai…

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

If two parallel lines are cut by a transversal , then each pa…

If two parallel lines are cut be a transversal, then each pai…

Postulate 3.1 Corresponding Angles Pos…

If two parallel lines are cut be a transversal, then each pai…

Theorem 3.1 Alternate Interior Angles…

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

Postulate 3-1

Theorem 3-1

Theorem 3-2

Theorem 3-3

Corresponding Angles Postulate... If a transversal intersects tw…

Alternate Interior Angles Theorem... If a transversal intersects…

Same-Side Interior Angles Theorem... If a transversal intersects…

Alternate Exterior Angles Theorem... If a transversal intersects…

Postulate 3-1

Corresponding Angles Postulate... If a transversal intersects tw…

Theorem 3-1

Alternate Interior Angles Theorem... If a transversal intersects…

If a transversal intersects two parall…

If a transversal intersects two parall…

If a transversal intersects two parall…

If a transversal intersects two parall…

Same-Side Interior Angles Postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parall…

Same-Side Interior Angles Postulate

If a transversal intersects two parall…

Alternate Interior Angles Theorem

Corresponding Angles Postulate (Theore…

Alternate Interior Angles Theorem (The…

Alternate Exterior Angles Theorem (The…

Consecutive Interior Angles Theorem (T…

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 Angles Postulate (Theore…

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

Alternate Interior Angles Theorem (The…

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

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 (II)

Perpendicular lines

skew lines

parallel planes

coplanar and do not intersect

intersect at 90 degree angles

not coplanar skew lines are not parallel and do not intersect

planes that do not interect

parallel lines (II)

coplanar and do not intersect

Perpendicular lines

intersect at 90 degree angles

P 3.1 Corresponding Angles Postulate

T 3.1 Alternate Interior Angles Theorem

T 3.2 Consecutive Interior Angles Theo…

T 3.3 Alternate Exterior Angles Theorem

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 lines are cut by a transversal, then each pai…

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

P 3.1 Corresponding Angles Postulate

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

T 3.1 Alternate Interior Angles Theorem

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

Theorem 3.1

Theorem 3.2

Theorem 3.3

Postulate 15

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

If two sides of two adjacent acute angle are perpendicular, t…

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

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

Theorem 3.1

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

Theorem 3.2

If two sides of two adjacent acute angle are perpendicular, t…

AIA

SSI

CA

AEA

Alternate Interior Angles- angles on opposite sides of the tr…

Same Side Interior- angles found on the same side of the tran…

Corresponding Angles- Angles that are in the same position re…

Alternate Exterior Angles- Angles on opposite sides of the tr…

AIA

Alternate Interior Angles- angles on opposite sides of the tr…

SSI

Same Side Interior- angles found on the same side of the tran…

postulate 3.1: Corresponding Angles Po…

theorem 3.1: Alternate Interior Angles…

theorem 3.2: Consecutive Interior Angl…

theorem 3.3: Alternate Exterior Angles…

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 lines are cut by a transversal, then each pai…

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

postulate 3.1: Corresponding Angles Po…

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

theorem 3.1: Alternate Interior Angles…

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

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Theorem

Alternate Interior Angles Theorem

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

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

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

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

Parallel Postulate

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

Perpendicular Postulate

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

Parallel postulate

Perpendicular postulate

Corresponding angles postulate

Alternate interior angles theorem

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

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

If two parallel lines are cut by a transversal, then pairs of…

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

Parallel postulate

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

Perpendicular postulate

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

If two parallel lines are cut by a tra…

If two parallel lines are cut by a tra…

If two parallel lines are cut by a tra…

If two parallel lines are cut by a tra…

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 two…

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

If two parallel lines are cut by a tra…

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

If two parallel lines are cut by a tra…

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

Theorem 3-1

Postulate

Theorem 3-2

Theorem 3-3

2 || lines are intersected by a 3rd plane, the lines of inter…

If 2 parallel lines are cut by a transversal, the correspondi…

If 2 parallel lines are cut by a transversal, the alternating…

If 2 parallel lines are cut by a transversal, the alternating…

Theorem 3-1

2 || lines are intersected by a 3rd plane, the lines of inter…

Postulate

If 2 parallel lines are cut by a transversal, the correspondi…

Corresponding Angles Postulate

Same Side Interior Angles Theorem

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

when two parallel lines are cut by a transversal, then the co…

when two parallel lines are cut by a transversal, the same-si…

when two parallel lines are cut by a transversal, alternate i…

when two parallel lines are cut by a transversal alternate ex…

Corresponding Angles Postulate

when two parallel lines are cut by a transversal, then the co…

Same Side Interior Angles Theorem

when two parallel lines are cut by a transversal, the same-si…

Angle Measure Postulate a-e

a. Unique Measure Assumption

b. Unique Angle Assumption

c. Straight Angle Assumption

---

Every angle has a unique measure from 0 degrees to 180 degrees.

Given any ray, ray VA and a real number r between 0 and 180,…

If ray AV and ray AB are opposite rays, then m<VAB=180 degrees.

Angle Measure Postulate a-e

---

a. Unique Measure Assumption

Every angle has a unique measure from 0 degrees to 180 degrees.

Linear Pair Theorem

Verticle Angles Theorem

Reflexive Property of Equality

Symmetric Property of Equality

If two angles form a linear pair, then they are supplementary

If two angles are vertical angles, then their measures are eq…

a=a

If a=b, then b=a

Linear Pair Theorem

If two angles form a linear pair, then they are supplementary

Verticle Angles Theorem

If two angles are vertical angles, then their measures are eq…

Theorem 3-1

Postulate 10

Theorem 3-2

Theorem 3-3

if two parallel planes are cut by a third plane, then the lin…

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

if two parallel lines are cut but a transversal, then alterna…

if two parallel lines are cut by a transversal, then same-sid…

Theorem 3-1

if two parallel planes are cut by a third plane, then the lin…

Postulate 10

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

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Theorem

Alternate Interior Angles Theorem

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

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

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

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

Parallel Postulate

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

Perpendicular Postulate

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

Corresponding angles postulate

Alternate interior angles theorem

Alternate exterior angles theorem

Same-side interior angles theroem

If 2 parallel lines are cut by a transversal, then the two pa…

If 2 parallel lines are cut by a transversal, then the two pa…

If 2 parallel lines are cut by a transversal, then the two pa…

If 2 parallel lines are cut by a transversal, then the 2 pair…

Corresponding angles postulate

If 2 parallel lines are cut by a transversal, then the two pa…

Alternate interior angles theorem

If 2 parallel lines are cut by a transversal, then the two pa…

Parallel lines

Skew lines

Parallel planes

Transversal

Two lines are ____ if they are coplanar and do not intersect

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 are ____ if they are coplanar and do not intersect

Skew lines

Lines that do not intersect and are not coplanar

Distance Postulate

Ruler Postulate

Ruler Placement Postulate

Theorem 2-3

To every pair of different points there corresponds a unique…

The points of a line can be placed in correspondence with the…

Given two points P and Q of a line, the coordinate system can…

Let A, B and C be points of a line, with coordinates x,y, and…

Distance Postulate

To every pair of different points there corresponds a unique…

Ruler Postulate

The points of a line can be placed in correspondence with the…

Parallel intersection Theorem

Corresponding Angle Postulate

alternate interior angle theorem

same-side interior angles theorem

If two parallel planes are cut by a third plane then the line…

if two parallel lines are cut by a transversal then correspon…

if two parallel lines are cut by a transversal then alternate…

if two parallel lines are cut by a transversal then same-side…

Parallel intersection Theorem

If two parallel planes are cut by a third plane then the line…

Corresponding Angle Postulate

if two parallel lines are cut by a transversal then correspon…

Parallel Postualte

Perpendicular Postualte

Corresponding Angles Theorem

Alternate Interior Angles

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

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

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

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

Parallel Postualte

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

Perpendicular Postualte

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

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Consecutive Interior Angles Theorem

Alternate Exterior Angles Theorem

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 lines are cut by a transversal, then each pai…

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

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

Corresponding angles postulate

Anternate interior angles theorem

Alternate exterior angles theorem

Same side interior angles theorem

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

If two parallel lines are cut by a transversal, the pairs of…

If two parallel lines are cut by a transversal the pairs of a…

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

Corresponding angles postulate

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

Anternate interior angles theorem

If two parallel lines are cut by a transversal, the pairs of…

Corresponding Angles Postulate

Slopes of Parallel Lines

Slopes of Perpendicular Lines

Converse of Corresponding Angles Postu…

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

Two nonvertical lines have the same slope if and only if they…

Two nonvertical lines are perpendicular if and only if the pr…

If two lines are cut by a transversal so that corresponding a…

Corresponding Angles Postulate

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

Slopes of Parallel Lines

Two nonvertical lines have the same slope if and only if they…

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Same-Side Interior Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then correspo…

If a transversal intersects two parallel lines, then alternat…

If a transversal intersects two parallel lines, then same-sid…

If a transversal intersects two parallel lines, then alternat…

Corresponding Angles Postulate

If a transversal intersects two parallel lines, then correspo…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternat…

Corresponding Angles Postulate

Slopes of Parallel Lines

Slopes of Perpendicular Lines

Converse of Corresponding Angles Postu…

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

Two nonvertical lines have the same slope if and only if they…

Two nonvertical lines are perpendicular if and only if the pr…

If two lines are cut by a transversal so that corresponding a…

Corresponding Angles Postulate

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

Slopes of Parallel Lines

Two nonvertical lines have the same slope if and only if they…

Postulate 3-1

Theorem 3-1

Theorem 3-2

Theorem 3-3

If a transversal intersects 2 parallel lines then same side i…

If a transversal intersects 2 parallel lines then alternate i…

If a transversal intersects 2 parallel lines then correspondi…

If a transversal intersects 2 parallel lines then alternate e…

Postulate 3-1

If a transversal intersects 2 parallel lines then same side i…

Theorem 3-1

If a transversal intersects 2 parallel lines then alternate i…

The Isosceles Triangle Theorem: If two…

Isosceles Corollary 1: An equilateral…

Isosceles Corollary 2: An equilateral…

Isosceles Corollary 3: The bisector of…

the angles opposite those sides are congruent.

equiangular.

three 60 degree angles.

perpendicular to the base of it's midpoint.

The Isosceles Triangle Theorem: If two…

the angles opposite those sides are congruent.

Isosceles Corollary 1: An equilateral…

equiangular.

Same-Side Interior Angles Postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then same-sid…

If a transversal intersects two parallel lines, then alternat…

If a transversal intersects two parallel lines, then correspo…

If a transversal intersects two parallel lines then alternate…

Same-Side Interior Angles Postulate

If a transversal intersects two parallel lines, then same-sid…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternat…

Every angle has a measure between 0-180

If an angle is composed of opposite ra…

If the rays that compose and an angles…

Postulate that describes the various m…

Unique Measure Assumption

Straight Angle Assumption

Zero Angle Assumption

Angle Measure Postulate

Every angle has a measure between 0-180

Unique Measure Assumption

If an angle is composed of opposite ra…

Straight Angle Assumption

Same side interior angles postulate

Alternate interior angles theorem

Corresponding angles theorem

Alternate exterior angles theorem

2 interior angles on the same side of the transversal

Nonadjacent interior angles that lie on opposite sides of a t…

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

Angles that lie outside a pair of lines and on opposite sides…

Same side interior angles postulate

2 interior angles on the same side of the transversal

Alternate interior angles theorem

Nonadjacent interior angles that lie on opposite sides of a t…

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Same-Side Interior Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then the corr…

If a transversal intersects two parallel lines, then the alte…

If a transversal intersects two parallel lines, then the same…

If a transversal intersects two parallel lines, then the alte…

Corresponding Angles Postulate

If a transversal intersects two parallel lines, then the corr…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then the alte…

PTT

Theorem 3-9

CCAT

CAIAT

If n is perpendicular to l, and l is parallel to m, then n is…

If m is perpendicular to t, and n is perpendicular to t, then…

If <2 is congruent and corresponding to <6 on lines l and m a…

If <4 and <6 are congruent alternate interior angles on line…

PTT

If n is perpendicular to l, and l is parallel to m, then n is…

Theorem 3-9

If m is perpendicular to t, and n is perpendicular to t, then…

corresponding angles postulate

alternate interior angles theorem

same-side interior angles theorem

alternate exterior angles theorem

if a transversal intersects two parallel lines, then correspo…

if a transversal intersects two parallel lines, then alternat…

if a transversal intersects two parallel lines, then same-sid…

if a transversal intersects two parallel lines, then alternat…

corresponding angles postulate

if a transversal intersects two parallel lines, then correspo…

alternate interior angles theorem

if a transversal intersects two parallel lines, then alternat…

same side interior angle postulate

alternate interior angles theorem

corresponding angles theorem

alternate exterior angles theorem

if a transversal intersects two parallel lines, then same sid…

if a transversal intersects two parallel lines, then alternat…

if a transversal intersects two parallel lines, then correspo…

if a transversal intersects two parallel lines, then alternat…

same side interior angle postulate

if a transversal intersects two parallel lines, then same sid…

alternate interior angles theorem

if a transversal intersects two parallel lines, then alternat…

Reflexive Property

SSS postulate

SAS postulate

ASA postulate

Any segment or angle is congruent to itself

If three sides of one triangle are congruent to three sides o…

If two sides and the included angle of one triangle are congr…

If two angles and the included side of one triangle are congr…

Reflexive Property

Any segment or angle is congruent to itself

SSS postulate

If three sides of one triangle are congruent to three sides o…