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Law of Detatchment

Law of Syllogism

Postulate 1.1

Postulate 1.2

If p --> q is a true statement, and p is true, then q is true.

If p --> q, and q --> r, then p --> r.

Through any 2 points there exists exactly one line

If 2 distinct lines intersect, then they intersect in exactly…

Law of Detatchment

If p --> q is a true statement, and p is true, then q is true.

Law of Syllogism

If p --> q, and q --> r, then p --> r.

Law of Detatchment

Law of Syllogism

Postulate 1.1

Postulate 1.2

If p --> q is a true statement, and p is true, then q is true.

If p --> q, and q --> r, then p --> r.

Through any 2 points there exists exactly one line

If 2 distinct lines intersect, then they intersect in exactly…

Law of Detatchment

If p --> q is a true statement, and p is true, then q is true.

Law of Syllogism

If p --> q, and q --> r, then p --> r.

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line.

If two lines intersect, then they intersect in exactly one po…

If two planes intersect, then they intersect in exactly one l…

Through any three noncollinear points there is exactly one pl…

Postulate 1-1

Through any two points there is exactly one line.

Postulate 1-2

If two lines intersect, then they intersect in exactly one po…

Segment addition postulate

Angle addition postulate

Linear pair postulate

Area addition postulate

If 3 pt. Are Collinear Ab+Bc=ac

Angle AOB+BOC=AOC

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

The area of a region is the su. Of the areas of its nonoverla…

Segment addition postulate

If 3 pt. Are Collinear Ab+Bc=ac

Angle addition postulate

Angle AOB+BOC=AOC

Ruler Postulate

Segment Addition Postulate

Distance Formula

Protractor Postulate

The points on a line can be matched one to one with real numb…

If B is between A and C, then AB+BC=AC

The distance between A(x₁,y₁) and B(x₂,y₂) =√(x₂-x₁)+(y₂-y₁)

If point O is the center of a circle and points A and B are o…

Ruler Postulate

The points on a line can be matched one to one with real numb…

Segment Addition Postulate

If B is between A and C, then AB+BC=AC

Through any 2 points,

If 2 distinct lines intersect,

If 2 planes intersect,

Through any 3 non-collinear points,

there is exactly one line

then they intersect in exactly one point

then they intersect at exactly one line

there is exactly one plane

Through any 2 points,

there is exactly one line

If 2 distinct lines intersect,

then they intersect in exactly one point

Law of Detachment

Law of Syllogism

Segment Addition Postulate

Angle Addition Postulate

If p -> q is true and p is true, then q is true

If p -> q and q -> r, then p -> r

If points A, B, and C are collinear and B is between A and C,…

If point T is interior of ∠AXC, then m∠AXT + m∠TXC = m∠AXC

Law of Detachment

If p -> q is true and p is true, then q is true

Law of Syllogism

If p -> q and q -> r, then p -> r

1-1

1-2

1-3

1-4

Through any two points there in exactly one line

Two distinct lines intersect in exactly one point

If two distinct planes intersect, then they intersect in exac…

Through any non-collinear points, there is exactly one plane

1-1

Through any two points there in exactly one line

1-2

Two distinct lines intersect in exactly one point

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

All right angles are congruent

If <1 and <2 are supplementary and <3…

If <4 and <5 are complementary and <6…

vertical angles are congruent

right angles congruence theorem

Congruent Supplements Theorem

Congruent Complements Theorem

vertical angles congruence theorem

All right angles are congruent

right angles congruence theorem

If <1 and <2 are supplementary and <3…

Congruent Supplements Theorem

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Linear Pairs are Supplementary.

Perpendicular Lines form right angles.

All right angles are congruent.

Supplements of congruent angles are co…

Right

Supplementary (Working with total of 4 angles)

Linear Pairs are Supplementary.

Perpendicular Lines form right angles.

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

1-1

1-2

1-3

1-4

Through any two points there in exactly one line

Two distinct lines intersect in exactly one point

If two distinct planes intersect, then they intersect in exac…

Through any non-collinear points, there is exactly one plane

1-1

Through any two points there in exactly one line

1-2

Two distinct lines intersect in exactly one point

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent…

If 2 angles are complementary to the same angle or congruent…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

law of detachment

law of syllogism

postulate 5

postulate 6

if P implies Q is a true conditional statement and P is true,…

if P implies Q and Q implies R is true, then P implies R.

through any two points there exists exactly one line.

a line contains at least two points.

law of detachment

if P implies Q is a true conditional statement and P is true,…

law of syllogism

if P implies Q and Q implies R is true, then P implies R.

segment addition postulate

law of detachment

conditional statement

hypothesis

if SRT are collinear and R is between S and T then SR + RT= ST

if the hypothesis of a conditional statement is true then the…

a statement in the form of if______then______

"if" portion of a conditional statement

segment addition postulate

if SRT are collinear and R is between S and T then SR + RT= ST

law of detachment

if the hypothesis of a conditional statement is true then the…

Unique Line Postulate

Intersecting Lines Postulate

Intersecting Planes Postulate

Plane Postulate

Through any two points there is exactly one line

If two lines intersect, then they intersect in exactly one po…

If two planes intersect, then they intersect in exactly one l…

Through any three nonlinear points there is exactly one plane

Unique Line Postulate

Through any two points there is exactly one line

Intersecting Lines Postulate

If two lines intersect, then they intersect in exactly one po…

Corresponding Angles Converse

Alternate Interior Angles Converse

Alternative Exterior Angles Converse

Consecutive Interior Angles converse

If two lines are cut by a transversal so the corresponding an…

If two lines are cut by a transversal so the alternate interi…

if two lines are cut by a transversal so the alternate exteri…

If two lines are cut by a transversal so the consecutive inte…

Corresponding Angles Converse

If two lines are cut by a transversal so the corresponding an…

Alternate Interior Angles Converse

If two lines are cut by a transversal so the alternate interi…

Complementary angles

Supplementary angles

Theorem

Vertical Angles

two angles whose measures have a sum of 90°

two angles who measures have a sum of 180°

a statement that can be proven

two angles formed by intersecting lines and facing in the opp…

Complementary angles

two angles whose measures have a sum of 90°

Supplementary angles

two angles who measures have a sum of 180°

Segment Addition Postulate

Angle Addition Postulate

Definition of Midpoint & Bisector

Definition of Angle Bisector

If B is between A and C then the length of AC is equal to the…

If P is in the interior of ∠RST then the measure of ∠RST is t…

A bisector bisects a line segment at its midpoint which divid…

A ray that divides an angle into two adjacent angles that are…

Segment Addition Postulate

If B is between A and C then the length of AC is equal to the…

Angle Addition Postulate

If P is in the interior of ∠RST then the measure of ∠RST is t…

Law of detachment

Law of Syllogism

Reflexive Property

Symmetric Property

if p implies q is a true conditional statement and p is true…

if p implies q and q imply r are true conditional statements…

for any real number a, a=a

if a=b then b=a

Law of detachment

if p implies q is a true conditional statement and p is true…

Law of Syllogism

if p implies q and q imply r are true conditional statements…

segment addition postulate

reflexive property

congruent

midpoint theorem

AB + BC = AC

any segment or angle is congruent/equal to itself (AB = AB) (…

have equal measure

If AB + BC = AC and AB=BC

segment addition postulate

AB + BC = AC

reflexive property

any segment or angle is congruent/equal to itself (AB = AB) (…

The distance between two points is the…

If A, B, and C are collinear and B is…

If B is on the interior of ∠ADC, then…

Any line segment will have exactly one…

ruler postulate

segment addition postulate

angle addition postulate

midpoint postulate

The distance between two points is the…

ruler postulate

If A, B, and C are collinear and B is…

segment addition postulate

corresponding angles

congruent corresponding angles

SSS Postulate

SAS Postulate

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

If two lines are cut by a transversal and corresponding angle…

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

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

corresponding angles

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

congruent corresponding angles

If two lines are cut by a transversal and corresponding angle…

Perpendicular Bisector Theorem

Corresponding Angles Theorem

Alternate Interior Angles Theorem

Same-Side Interior Angles Postulate

If a point is on the perpendicular bisector of a segment, the…

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

If two parallels are cut by a transversal, then the pair of a…

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

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, the…

Corresponding Angles Theorem

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

Corresponding Angles Postulate (3-1)

Alternate Interior Angles Theorem (3-1)

Consecutive Interior Angles Theorem (3…

Alternate Exterior Angles Theorem (3-3)

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

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

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

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

Corresponding Angles Postulate (3-1)

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

Alternate Interior Angles Theorem (3-1)

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be paired with the real numbers in s…

If B is between A and C, then AB + BC = AC.

Given line AB and a point O on line AB, all rays that can be…

If B is in the interior of <AOC, then m<AOB + m<BOC = m<AOC.

Ruler Postulate

The points on a line can be paired with the real numbers in s…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC.

Postulate

Theorem

Intersection of 2 lines is exactly...

Intersection of 2 planes is exactly...

Statement accepted without proof

Conjecture (mathematical hypothesis) that has been proved

1 point

1 line

Postulate

Statement accepted without proof

Theorem

Conjecture (mathematical hypothesis) that has been proved

The distance between two points is the…

If A, B, and C are collinear and B is…

If B is on the interior of ∠ADC, then…

Any line segment will have exactly one…

ruler postulate

segment addition postulate

angle addition postulate

midpoint postulate

The distance between two points is the…

ruler postulate

If A, B, and C are collinear and B is…

segment addition postulate

Complementary angles

Supplementary angles

Theorem

Vertical Angles

two angles whose measures have a sum of 90°

two angles who measures have a sum of 180°

a statement that can be proven

two angles formed by intersecting lines and facing in the opp…

Complementary angles

two angles whose measures have a sum of 90°

Supplementary angles

two angles who measures have a sum of 180°

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with the real…

If B is between A and C, then AB+BC=AC.

The measure of ∠AOB, which can be written as m∠AOB, is equal…

If P is in the interior of ∠RST, then the measure of ∠RST is…

Ruler Postulate

The points on a line can be matched one to one with the real…

Segment Addition Postulate

If B is between A and C, then AB+BC=AC.

Segment Addition Postulate

Protractor Postulate

Parallel Lines

Skew Lines

AB + BC = AC

Says that you can measure any angle

two lines that don't intersect and are coplanar

two lines that don't intersect and aren't coplanar

Segment Addition Postulate

AB + BC = AC

Protractor Postulate

Says that you can measure any angle

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

1. The points on a line can be paired with the real numbers i…

If B is between A and C, then AB+BC=AC

On line AB in a given plane, choose any point O between A and…

If point B lies in the interior of <AOC, the m<AOB a m<BOC =…

Ruler Postulate

1. The points on a line can be paired with the real numbers i…

Segment Addition Postulate

If B is between A and C, then AB+BC=AC

Midpoint

Collinear

Straight Angles

Acute Angles

It is a midpoint if and only if it divides a segment into two…

3 or more points on the same line

The sides of a straight angle form a line

Acute angles are less than a right angle

Midpoint

It is a midpoint if and only if it divides a segment into two…

Collinear

3 or more points on the same line

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…

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 pos.

perpendicular pos.

paragraph proof

transitive property of parallel lines

if there is a line and a point not on that line then there is…

if there is a line and a point not on that line then there is…

a proof written as a paragraph

if two lines are parallel to the same line then they are para…

parallel pos.

if there is a line and a point not on that line then there is…

perpendicular pos.

if there is a line and a point not on that line then there is…

(2-4)Definition of midpoint:

(3-9)Definition of bisector:

(5-2)CPCF Theorem (segment):

(2-4)Definition of a circle:

If a point is the midpoint of a segment, it divides the segme…

If a figure is the the bisector of a segment, it divides the…

If figures are congruent, then corresponding segments are con…

If a figure is a circle, then its radii are congruent. (2-4)

(2-4)Definition of midpoint:

If a point is the midpoint of a segment, it divides the segme…

(3-9)Definition of bisector:

If a figure is the the bisector of a segment, it divides the…

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Segment addition postulate

Angle addition postulate

Postulate 5

Postulate 6

If B is between A and C, then AB + BC = AC

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

A line contains at least two points; a plane contains at leas…

Through any two points there is exactly one line.

Segment addition postulate

If B is between A and C, then AB + BC = AC

Angle addition postulate

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

Postulate - 2.1

Postulate - 2.2

Postulate - 2.3

Postulate - 2.4

Through any two points, there is exactly one line

Through any three non collinear points, there is exactly one…

A line contains at least two points

A plane contains at least three non collinear points

Postulate - 2.1

Through any two points, there is exactly one line

Postulate - 2.2

Through any three non collinear points, there is exactly one…

If there are two points,

If there is a line,

Two points determine a ____

If there are three noncollinear points,

there is exactly one line that contains them.

then there are at least two points on the line

line

there is exactly one plane that contains them

If there are two points,

there is exactly one line that contains them.

If there is a line,

then there are at least two points on the line

theorem

postulate

definition

geometry

a statement that can be proved

something we don't need to prove, uses past information to ba…

assigns a term to an object. are always reversible

to take a series of facts to put in a logical way to reach a…

theorem

a statement that can be proved

postulate

something we don't need to prove, uses past information to ba…

Parallel Lines

Perpendicular Lines

Skew Lines

Parallel Planes

Are coplanar lines and do not intersect.

Lines that intersect at 90 degree angles.

Lines that are not coplanar, not parallel, and do not interse…

Are planes that do not intersect.

Parallel Lines

Are coplanar lines and do not intersect.

Perpendicular Lines

Lines that intersect at 90 degree angles.

Same side interior angles postulate

Same side exterior angles postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

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

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

If t intersects two parallel lines, then alternate interior a…

If t intersects two parallel lines, then corresponding angles…

Same side interior angles postulate

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

Same side exterior angles postulate

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

addition property of equality

subtraction property of equality

multiplication property of equality

division property of equality

if a=b, then a+c=b+c

if a=b, then a-c=b-c

if a=b, then ac=bc

if a=b AND c≠0, then a/c=b/c

addition property of equality

if a=b, then a+c=b+c

subtraction property of equality

if a=b, then a-c=b-c

Definitions

Complementary Angles

Supplementary angles

theorem

Definitions

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

Definitions

Definitions

Complementary Angles

Two angles whose measures equal 90 degrees