# Study sets matching "honors theorems postulates geometry postulates theorems"

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ruler postulate 1-2-1

segment addition postulate

protractor postulate

angle addition postulate

the points on a line can be put to a one-to-one correspondence…

in order to say that a point is between 2 other points, then a…

all rays can be drawn from point O and put into a one-to-one c…

ruler postulate 1-2-1

the points on a line can be put to a one-to-one correspondence…

segment addition postulate

in order to say that a point is between 2 other points, then a…

*Through any two points...

* If two lines intersect...

*If two planes intersect...

*Through any three noncollinear points.…

...there is exactly one line

...then they intersect in exactly one point

...then they intersect in exactly one line

...there is exactly one plane

*Through any two points...

...there is exactly one line

* If two lines intersect...

...then they intersect in exactly one point

Through any two points...

Through any three noncollinear points...

A line consists of...

A plane contains at least...

there is exactly one line

there is exactly one plane

a least 2 points

3 noncollinear points

Through any two points...

there is exactly one line

Through any three noncollinear points...

there is exactly one plane

segment addition postulate

reflexive property

congruent

midpoint theorem

AB + BC = AC

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

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) (m…

Parallel Lines (||)

Parallel Planes

Skew

Transversal

2 lines that never intersect

2 planes that never intersect

lines which are not coplanar and do not intersect

a line which intersects 2 or more lines

Parallel Lines (||)

2 lines that never intersect

Parallel Planes

2 planes that never intersect

Determining a Line Postulate

Bet. of Points Thm.

Bet. of Rays Thm.

Half Corollary to the Definition of Bis…

2 points determine a line

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

If ray OB is between rays OA and OC, then <AOB + BOC = AOC

If something is being bisected, then a portion of it is equal…

Determining a Line Postulate

2 points determine a line

Bet. of Points Thm.

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

Postulate 2/Segment Addition Postulate

congruent

congruent segments

midpoint of a segment

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

the term used to describe two objects with the same size and s…

segments that have equal lengths

the point that divides a segment into two congruent segments

Postulate 2/Segment Addition Postulate

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

congruent

the term used to describe two objects with the same size and s…

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

Parallel Postulate

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

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

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

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

Segment Addition Postulate

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

Angle Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Corresponding Angles Postulate

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

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

On AB is a given plane, choose any point O between A and B. Co…

If m is parallel to n with a transversal intersecting both, th…

Ruler Postulate

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

Segment Addition Postulate

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

Inductive Reasoning

Conjecture

Counterexample

Statement

logic used to reach a conclusion or conjecture

A conclusion that is maybe true or false

example that shows that a conjecture is false

a sentence that can be either True or False

Inductive Reasoning

logic used to reach a conclusion or conjecture

Conjecture

A conclusion that is maybe true or false

3 undefined terms

Definitions

Postulates

Theorems

Point, line, plane

-Stated for ideas, as clear and exact as possible... -Establish t…

-simplest and most fundamental statements ... -Given WITHOUT PROO…

Statements that are proven ... -When proven, you show that it fol…

3 undefined terms

Point, line, plane

Definitions

-Stated for ideas, as clear and exact as possible... -Establish t…

If two angles are right angles, then th…

If two angles are straight angles, then…

If angles or segments are congruent to…

If angles or segments are congruent to…

Theorem

Theorem

Theorem

Theorem

If two angles are right angles, then th…

Theorem

If two angles are straight angles, then…

Theorem

Ruler Postulate

Segment Addition Postulate

Angle Addition Postulate

True

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

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

If D is in the interior of Angle ABC, then... (meas.)angle ABD +…

State whether the following statement is true or false: ... Throu…

Ruler Postulate

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

Segment Addition Postulate

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

altitude of a triangle

circumcenter of a triangle

incenter of a triangle

orthocenter of a triangle

a perpendicular segment from a vertex to the line containing t…

the point of concurrency of the perpendicular bisectors of a t…

the point of concurrency of the angle bisectors of a triangle

the point of concurrency of the three altitudes of a triangle

altitude of a triangle

a perpendicular segment from a vertex to the line containing t…

circumcenter of a triangle

the point of concurrency of the perpendicular bisectors of a t…

The Ruler Postulate

The Protractor Postulate

Segment Addition Postulate/The Betweenn…

Angle Addition Postulate/The Betweennes…

points on a line can be numbered so that positive number diffe…

you can measure angles

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

∠AOB + ∠BOC = ∠AOC

The Ruler Postulate

points on a line can be numbered so that positive number diffe…

The Protractor Postulate

you can measure angles

Point

Line

Plane

Collinear

Names a location and has no size, represented by a dot... ex. Poi…

A straight path that has no thickness and extends forever... ex.…

A flat surface that has no thickness and extends forever... Ex. P…

Points that lie on the same line

Point

Names a location and has no size, represented by a dot... ex. Poi…

Line

A straight path that has no thickness and extends forever... ex.…

What is the difference between a postul…

Definition of Congruence

Segment Addition Postulate

Angle Addition Postulate

A postulate is something that cannot be proven.

if angles have equal measures, then they're congruent

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

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

What is the difference between a postul…

A postulate is something that cannot be proven.

Definition of Congruence

if angles have equal measures, then they're congruent

congruent by the ss congruence postulate

regular

base angles

segment

if three sides of one triangle are congruent to three sides of…

a __________ polygon is both equiangular and equilateral

if two sides of a triangle are congruent, then the ________ ar…

a __________ is the part of a line consisting of two endpoints…

congruent by the ss congruence postulate

if three sides of one triangle are congruent to three sides of…

regular

a __________ polygon is both equiangular and equilateral

Theorem 9-1

Corollary (of Theorem 9-1)

Theorem 9-2

postulate 16

If a line is tangent to a circle, then the line is perpendicul…

Tangents to a circle from a point are congruent.

If a line in the plane of a circle is perpendicular to a radiu…

measure of the arc formed by two adjacent arcs is the sum of t…

Theorem 9-1

If a line is tangent to a circle, then the line is perpendicul…

Corollary (of Theorem 9-1)

Tangents to a circle from a point are congruent.

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 ang…

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

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

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

Corresponding Angles Converse

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

Alternate Interior Angles Converse

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

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement (if-then statement), the statement…

A statement written in an if then form... A statement of the form…

An educated guess based on known information... pg 78

The statement formed by negating both the hypothesis(educated…

Conclusion

In a conditional statement (if-then statement), the statement…

Conditional Statement

A statement written in an if then form... A statement of the form…

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

Parallel Postulate

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

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

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

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

Segment Addition Postulate

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

Angle Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Angle Addition Postulate

True

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

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

If D is in the interior of Angle ABC, then... (meas.)angle ABD +…

State whether the following statement is true or false: ... Throu…

Ruler Postulate

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

Segment Addition Postulate

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

Angle-Side-Angle Congruence Theorem (AS…

Postulate

Theorem

Angle-Angle-Side Congruence Theorem (AA…

If two angles and a side between them are congruent in two dif…

A rule that we accept to be true.

A rule that has been proven to be true.

If two angles and a side not between them are congruent in two…

Angle-Side-Angle Congruence Theorem (AS…

If two angles and a side between them are congruent in two dif…

Postulate

A rule that we accept to be true.