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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…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider Ray OB and a point A on one side of Ray OB. The rays…

If P is in the interior of <RST, then m<RST + m<RSP = m<PST

Ruler Postulate

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

Segment Addition Postulate

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

Reflexive

Symmetric

Transitive

Segment Addition Postulate

Line segment AB is congruent to line segment CD

If line segment AB is congruent to line segment CD, then line…

If line segment AB is congruent to line segment CD, and line…

Two segments of a line added together to get the length of th…

Reflexive

Line segment AB is congruent to line segment CD

Symmetric

If line segment AB is congruent to line segment CD, then line…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider Ray OB and a point A on one side of Ray OB. The rays…

If P is in the interior of <RST, then m<RST + m<RSP = m<PST

Ruler Postulate

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

Segment Addition Postulate

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

Congruent segments:

Congruent angles:

Midpoint:

Segment bisector:

segments whose lengths are equal

angles whose measures are equal

a point that divides a segment into 2 congruent segments

line (or part of a line) that intersects the segment at it's…

Congruent segments:

segments whose lengths are equal

Congruent angles:

angles whose measures are equal

point

line

plane

collinear

a location; has no length, no width, no thickness

extends in one dimension; has length but no width and no thic…

A flat surface that has length and width but no thickness

Points that lie on the same line.

point

a location; has no length, no width, no thickness

line

extends in one dimension; has length but no width and no thic…

Congruent Segments

Congruent Angles

Midpoint

Segment Bisector

Segments whose lengths are equal.

Angles whose measures are equal.

Point that divides a segment into 2 congruent segments.

Line (or part of a line) that intersects the segment at its m…

Congruent Segments

Segments whose lengths are equal.

Congruent Angles

Angles whose measures are equal.

postulate/axiom

postulate 1-1

postulate 1-2

postulate 1-3

an accepted statement of fact (basic building blocks of a log…

though any 2 there is exactly one line

if 2 district lines intersect then they intersect in exactly…

if 2 distinct planes intersect then they intersect in exactly…

postulate/axiom

an accepted statement of fact (basic building blocks of a log…

postulate 1-1

though any 2 there is exactly one line

ruler postulate

Segment Addition Postulate (Seg. Add.…

Protractor Postulate

Angle Addition Postulate

1.)points must be put on a number line... 2.)the distance betwee…

if B is between A and C, then AB+BC=AC (page 12 in book)

used to find the measure of an angle... 1.) take the absolute va…

m<AOB + m<BOC = m< AOC

ruler postulate

1.)points must be put on a number line... 2.)the distance betwee…

Segment Addition Postulate (Seg. Add.…

if B is between A and C, then AB+BC=AC (page 12 in book)

Postulate 1-1 Through any two points,…

Postulate 1-2 If two distinct lines in…

Postulate 1-3 If two distinct _______i…

Postulate 1-4 Through any ________poin…

line

point

planes

three noncollinear

Postulate 1-1 Through any two points,…

line

Postulate 1-2 If two distinct lines in…

point

collinear points

coplanar

parallel lines

parallel planes

Points that lie on the same line.

points that lie on the same plane

coplanar lines that do not intersect

planes that do not intersect.

collinear points

Points that lie on the same line.

coplanar

points that lie on the same plane

point

line

plane

collinear

a location; has no length, no width, no thickness

extends in one dimension; has length but no width and no thic…

A flat surface that has length and width but no thickness

Points that lie on the same line.

point

a location; has no length, no width, no thickness

line

extends in one dimension; has length but no width and no thic…

Same Side Interior Angles Postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Alternate Exterior Angles Theorem

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

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 Angles Postulate

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

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternat…

Postulate 1

Postulate 2

The Ruler Postulate (Postulate 3)

The Protractor Postulate (Postulate 4)

Two points determine a unique straight line.

Three noncollinear points determine a unique plane

a. To every point on a line there corresponds exactly one rea…

a. The rays in a half rotation (180 degrees) can be numbered…

Postulate 1

Two points determine a unique straight line.

Postulate 2

Three noncollinear points determine a unique plane

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…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider Ray OB and a point A on one side of Ray OB. The rays…

If P is in the interior of <RST, then m<RST + m<RSP = m<PST

Ruler Postulate

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

Segment Addition Postulate

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

Congruent Segments

Congruent Angles

Midpoint

Segment Bisector

line segments that have the same length.

angles that have the same length.

a point that divides the segment into congruent segments.

a point, ray, line, line segment, or plane that intersects th…

Congruent Segments

line segments that have the same length.

Congruent Angles

angles that have the same length.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider Ray OB and a point A on one side of Ray OB. The rays…

If P is in the interior of <RST, then m<RST + m<RSP = m<PST

Ruler Postulate

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

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

If you take a line segment and divide it into equal segments…

If B is between A and C, then AB + BC = AC (the parts add up…

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

If point B lies in the interior of /_AOC, then the m/_AOB + m…

Ruler Postulate

If you take a line segment and divide it into equal segments…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC (the parts add up…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider Ray OB and a point A on one side of Ray OB. The rays…

If P is in the interior of <RST, then m<RST + m<RSP = m<PST

Ruler Postulate

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

Segment Addition Postulate

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

Point

Line

Plane

Segment

Names a location and has no size. It is represented by a dot

A straight path that has no thickness and extends forever

A flat surface that has no thickness and extends forever

The part of a line consisting of two points and all points be…

Point

Names a location and has no size. It is represented by a dot

Line

A straight path that has no thickness and extends forever

points existence postulate

straight line postulate

plane postulate

flat plane postulate

space contains at least four noncoplanar points. every plane…

two points are contained in one and only one line (two points…

three noncollinear points are contained in one and only one p…

if two points are in a plane, then the line containing the po…

points existence postulate

space contains at least four noncoplanar points. every plane…

straight line postulate

two points are contained in one and only one line (two points…

Congruent Segments

Congruent Angles

Midpoint

Segment bisector

Segments whose lengths are equal

Angles whose measures are equal

Point that divides a segment into 2 congruent segments

Line (or part of a line) that intersects the segments at its…

Congruent Segments

Segments whose lengths are equal

Congruent Angles

Angles whose measures are equal

Non-Vertical Lines Parallel Line Theorem

Non-Vertical Lines Perpendicular Line…

Segment Addition Postulate

Angle Addition Postulate

Two non-vertical are parallel lines if and only if their slop…

Two non-vertical lines are perpendicular if and only if the p…

Let A, B, & C, be collinear points. If B is between A & C, th…

If Point S is in the interior of Angle PQR, then m∠PQS + m∠SQ…

Non-Vertical Lines Parallel Line Theorem

Two non-vertical are parallel lines if and only if their slop…

Non-Vertical Lines Perpendicular Line…

Two non-vertical lines are perpendicular if and only if the p…

Inductive Reasoning

Conjecture

Counterexample

Point

Reasoning based on patterns you observe

A conclusion you reach using inductive reasoning

An example for which the conjecture is incorrect

A location

Inductive Reasoning

Reasoning based on patterns you observe

Conjecture

A conclusion you reach using inductive reasoning

Inductive reasoning

Conjecture

Counter example

Point

A form of reasoning in which a conclusion is reached on a pat…

Appears to be true but isn't proven

Disproves a statement or proposition

A location, it has no size or width and is marked as a dot

Inductive reasoning

A form of reasoning in which a conclusion is reached on a pat…

Conjecture

Appears to be true but isn't proven

Congruent Segments

Congruent Angles

Midpoint

Segment bisector

Segments whose length are equal

Angles whose measures are equal

Point that divides a segment into 2 congruent segments

Line (or part of a line) that intersects the segment at its m…

Congruent Segments

Segments whose length are equal

Congruent Angles

Angles whose measures are equal

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

accepted rule that a ruler can find a distance

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

the measure of an angle is equal to the absolute value of the…

if P is in the interior of the angle RST, then the measure of…

Ruler Postulate

accepted rule that a ruler can find a distance

Segment Addition Postulate

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

Equilateral triangle

Equiangular triangle

Acute triangle

Scalene triangle

Triangle with all sides congruent

Triangle with all angles congruent

Triangle in which all sides are less than 90 degrees

Triangle with no two congruent sides

Equilateral triangle

Triangle with all sides congruent

Equiangular triangle

Triangle with all angles congruent

Reflexive

Symmetric

Transitive

Segment Addition Postulate

Line segment AB is congruent to line segment CD

If line segment AB is congruent to line segment CD, then line…

If line segment AB is congruent to line segment CD, and line…

Two segments of a line added together to get the length of th…

Reflexive

Line segment AB is congruent to line segment CD

Symmetric

If line segment AB is congruent to line segment CD, then line…

Point

Line

Plane

Space

Dot, has no size, named using capital letters, just posistion

Represented with arrowheads, infinite, no thickness

No thickness, infinite in all directions

Set of all points

Point

Dot, has no size, named using capital letters, just posistion

Line

Represented with arrowheads, infinite, no thickness

ruler postulate

Segment Addition Postulate (Seg. Add.…

Protractor Postulate

Angle Addition Postulate

1.)points must be put on a number line... 2.)the distance betwee…

if B is between A and C, then AB+BC=AC (page 12 in book)

used to find the measure of an angle... 1.) take the absolute va…

m<AOB + m<BOC = m< AOC

ruler postulate

1.)points must be put on a number line... 2.)the distance betwee…

Segment Addition Postulate (Seg. Add.…

if B is between A and C, then AB+BC=AC (page 12 in book)

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulates

Distance between two points A and B on a line can be found by…

If B is between AC, then AB + BC = AC

Think about protractor :)

If C is the interior angle of AOD, then ∠AOD = ∠AOC + ∠COD

Ruler Postulate

Distance between two points A and B on a line can be found by…

Segment Addition Postulate

If B is between AC, then AB + BC = AC

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider Ray OB and a point A on one side of Ray OB. The rays…

If P is in the interior of <RST, then m<RST + m<RSP = m<PST

Ruler Postulate

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

Segment Addition Postulate

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

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…

If _______ lines are parallel to the _…

In a plane, if a line is perpendicular…

If 2 parallel lines are cut by a _____…

If 2 parallel lines are cut by a _____…

2; same; parallel

perpendicular

transversal; congruent; alternate exterior anglr postulate

transversal; supplementary; same-side exterior angle theorem

If _______ lines are parallel to the _…

2; same; parallel

In a plane, if a line is perpendicular…

perpendicular

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Given two points, there corresponds a unique positive number…

Given two rays, there corresponds a unique positive number ca…

Ruler Postulate

Given two points, there corresponds a unique positive number…

Segment Addition Postulate

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. If AB + BC = AC,…

Consider ray OB and a point A on one side of of ray OB. The r…

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

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. If AB + BC = AC,…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Through any two points there is exactly one line

If two lines intersect they intersect in exactly one point

If two planes intersect, they intersect in exactly one line

Through any three non-collinear points there exists exactly o…

Postulate 1

Through any two points there is exactly one line

Postulate 2

If two lines intersect they intersect in exactly one point

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.

Postulate 1- Ruler Postulate

Postulate 2- Segment Addition Postulate

Postulate 3

Postulate 4- Angle Addition Postulate

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

ex. if B is between A and C then: AB+BC=AC

rays can be paired with the real numbers from 1-180

if a point lies in the interior of and angle, then you would…

Postulate 1- Ruler Postulate

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

Postulate 2- Segment Addition Postulate

ex. if B is between A and C then: AB+BC=AC

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be match one to one with real number…

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

Consider a point A on one side of line OB. The rays of a form…

If P is in the interior of ∠RST, then m∠RSP+m∠PST=m∠RST.

Ruler Postulate

The points on a line can be match one to one with real number…

Segment Addition Postulate

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

Postulate(a statement that is accepted…

Postulate 2

Postulate 3, postulate 4

Postulate 5

The points on a line can be paired in a one-to-one correspond…

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

Please see the text book for diagram explanation

Through any two points there is exactly one line

Postulate(a statement that is accepted…

The points on a line can be paired in a one-to-one correspond…

Postulate 2

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

ruler postulate

segment addition postulate

protractor postulate

angle addition postulate

the points on a line can paired in a one-to-one correspondenc…

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

given a point X on line PR, consider rays XP and XR as well a…

if point D is in the interior of angle ABC, then m angleABD +…

ruler postulate

the points on a line can paired in a one-to-one correspondenc…

segment addition postulate

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

Postulate 1 - Ruler Postulate

Postulate 2 - Segment Addition Postulate

Postulate 3 - Protractor Postulate

Postulate 4 - 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 ... AND ... If AB + BC =…

<AOB is equal to the absolute value of the difference between…

If B is the interior of angle AOC, then the measure of angle…

Postulate 1 - Ruler Postulate

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

Postulate 2 - Segment Addition Postulate

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