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

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

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

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

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

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

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…

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) (…

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 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

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

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

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.

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

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

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

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…

(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…

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…

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…

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 =…

Theorems

Postulates

Triangle Congruency

Postulate 1

Something that is provable

Things you cannot mathematically prove but are nonetheless true

SSS, ASA, SAS, AAS, HL

(Ruler Postulate)... The points on a line can be paired with rea…

Theorems

Something that is provable

Postulates

Things you cannot mathematically prove but are nonetheless true

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…

Linear Pair Postulate

Law of Detachment (word definition)

Law of Detachment (symbolic form)

Law of Syllogism (symbolic form)

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

If the hypothesis of a true conditional is true, then the con…

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

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

Linear Pair Postulate

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

Law of Detachment (word definition)

If the hypothesis of a true conditional is true, then the con…

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

Complementary Angles

Supplementary angles

theorem

Vertical angles

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

4 angles formed by intersecting lines and facing in four diff…

Complementary Angles

Two angles whose measures equal 90 degrees

Supplementary angles

two angles whose measures equal 180 degrees

Triangle Sum Theorem

Exterior Angle Theorem

Exterior Angle Inequality Theorem

Triangle Inequality Theorem

the sum of the measures of the interior angles of a triangle…

the measure of an exterior angle of a triangle is equal to th…

the measure of an exterior angle of a triangle is greater tha…

the sum of the lengths of any 2 sides of a triangle is greate…

Triangle Sum Theorem

the sum of the measures of the interior angles of a triangle…

Exterior Angle Theorem

the measure of an exterior angle of a triangle is equal to th…

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 for…

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 for…

Postulates points, planes, and lines

Postulates- intersection of planes and…

Ruler Postulate

Segment Addition Postulate

1.) Through any two pointd there is exactly one line.... 2.) Thr…

4.) If two lines intersect, then they intersect at one point.…

Points on a line can b put to a one to one correspondence wit…

If a point is in between two points then the distance from fi…

Postulates points, planes, and lines

1.) Through any two pointd there is exactly one line.... 2.) Thr…

Postulates- intersection of planes and…

4.) If two lines intersect, then they intersect at one point.…

parallel lines

skew lines

parallel planes

transversal

Two lines that 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 that are coplanar and do NOT intersect.

skew lines

Lines that do NOT intersect and are NOT coplanar.

Ruler Postulate

Segment Addition Postulate

Midpoint Formula

Distance Formula

Distance between points A and B (AB) is the absolute value of…

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

If A (x1,y1) and B(x2,y2) are points in a coordinate plane, t…

If A (x1,y1) and B (x2,y2) are points in a coordinate plane,…

Ruler Postulate

Distance between points A and B (AB) is the absolute value of…

Segment Addition Postulate

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

Complementary Angles

Supplementary angles

theorem

Vertical angles

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

4 angles formed by intersecting lines and facing in four diff…

Complementary Angles

Two angles whose measures equal 90 degrees

Supplementary angles

two angles whose measures equal 180 degrees

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

Postulate 1

Postulate 4

Postulate 5

Postulate 6

(Segment Addition Postulate)... if B is between A and C, then AB…

(Angle Addition Postulate)... if B lies in the interior of <AOC,…

a LINE contains at least 2 POINTS... a PLANE contains at least 3…

through any 2 POINTS there is exactly 1 LINE

Postulate 1

(Segment Addition Postulate)... if B is between A and C, then AB…

Postulate 4

(Angle Addition Postulate)... if B lies in the interior of <AOC,…

AAA Similarity Polstulate

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

If two angles of one triangle are congruent to two angles of…

If an angle of one triangle is congruent to an angle of anthe…

If the corresponding sides of two triangles are in proportion…

If a line parallel to a side of a triangle intersects the oth…

AAA Similarity Polstulate

If two angles of one triangle are congruent to two angles of…

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anthe…

Postulate

Conjecture

Truth Value

Conditional Statement

A statement that doesn't have to be proven and is always true.

Idea based on observation.

Conditional statements truth value of either false or true.

Statement that is written in the form of:... "If p, then q."... "p"…

Postulate

A statement that doesn't have to be proven and is always true.

Conjecture

Idea based on observation.

Any segment or angle is congruent to i…

If there exists a correspondence betwe…

If there exists a correspondence betwe…

If there exists a correspondence betwe…

Reflexive Property

Side-Side-Side Congruence (SSS)

Side-Angle-Side Congruence (SAS)

Angle-Side-Angle Congruence (ASA)

Any segment or angle is congruent to i…

Reflexive Property

If there exists a correspondence betwe…

Side-Side-Side Congruence (SSS)

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