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Study sets matching "geometry theorems and definitions postulates properties"

18 terms
Geometry: Definitions, Postulates, Properties and Theorems
Definition of Midpoint
Definition of Bisector
Definition of Angle Bisector
Definition of Perpendicular
The point halfway between two given points.
A line segment, line, or plane that divides a geometric figur…
A line or ray that divides an angle in half.
Two lines bisect and form a 90 degree angle.
Definition of Midpoint
The point halfway between two given points.
Definition of Bisector
A line segment, line, or plane that divides a geometric figur…
20 terms
Geometry Theorems, Properties, Postulates and Definitions
Complementary Angles
Supplementary Angles
Vertical Angles
Transversal
Angles that add up to 90 degrees
Angles that add up to 180 degrees
Two angles across from each other when lines intersect
A line that intersects two parallel lines
Complementary Angles
Angles that add up to 90 degrees
Supplementary Angles
Angles that add up to 180 degrees
Geometry Properties, Definitions, Theorems, and Postulates
Ruler Postulate
Segment Addition Postulate
Definition of a midpoint of a segment
Definition of a bisector of a segment
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
The point that divides the segment into two congruent segment…
The line, segment, ray, or plane that intersects the segment…
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
20 terms
Geometry Definitions, Postulates, Properties, & Theorems
Definition of congruent segments
Definition of congruent angles
Definition of right angle
Definition of linear pair
1. If segments are congruent, then they have the same measure…
1. If angles are congruent, then they have the same measure.…
1. If an angle has a measure of 90 degrees, then it is a righ…
1. If angles are adjacent angles and are formed by opposite r…
Definition of congruent segments
1. If segments are congruent, then they have the same measure…
Definition of congruent angles
1. If angles are congruent, then they have the same measure.…
59 terms
Geometry Properties, Theorems, Definitions, and Postulates
Addition Property of Equality (POE)
Subtraction Property of Equality (POE)
Multiplication Property of Equality (P…
Division Property of Equality (POE)
If a = b and c =d, then a + c = b + d
If a = b and c = d, then a - c = b - d
If a = b, then ac = cb
If a = b and c ≠ 0, then a/c = b/c
Addition Property of Equality (POE)
If a = b and c =d, then a + c = b + d
Subtraction Property of Equality (POE)
If a = b and c = d, then a - c = b - d
114 terms
Geometry Definitions/Postulates/Theorems/Properties
Segment Addition Postulate
Angle Addition Postulate
Conditional Definition
Definition of Linear Pair
If B is between A and C, then AB + BC = AC
If P is in the interior of angle RST, then angle RSP + angle…
If p then q
When the non shared sides of two adjacent angles form opposit…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate
If P is in the interior of angle RST, then angle RSP + angle…
51 terms
Geometry Properties, Theorems, Definitions, and Postulates
Segment Addition Postulate
Angle Addition Postulate (Pt. 1)
Angle Addition Postulate (Pt. 2)
Midpoint Theorem
If B is between A and C, then AB + BC = AC
If B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m∠AOC
If ∠AOC = 180° and B is any point not on ↔AC, then m∠AOC + m∠…
If M is the midpoint of line segment AB, then AM= 1/2 AB and…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate (Pt. 1)
If B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m∠AOC
114 terms
Geometry Definitions/Postulates/Theorems/Properties
Segment Addition Postulate
Angle Addition Postulate
Conditional Definition
Definition of Linear Pair
If B is between A and C, then AB + BC = AC
If P is in the interior of angle RST, then angle RSP + angle…
If p then q
When the non shared sides of two adjacent angles form opposit…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate
If P is in the interior of angle RST, then angle RSP + angle…
29 terms
Geometry Properties, Theorems, Postulates, Definitions
Reflexive Property
Transitive Property
Subtraction Property
Congruent Supplements Theorem
Any quantity is equal/congruent to itself.
If a=b and b=c, then a=c.
If a=b and c=d, then a-c=b-d. When equal quantities are subtr…
If two angles are supplements of the same angle (or of congru…
Reflexive Property
Any quantity is equal/congruent to itself.
Transitive Property
If a=b and b=c, then a=c.
86 terms
Geometry Definitions, Theorems, Properties, and Postulates
Identity Properties
Commutative Properties
Associative Properties
Inverse Properties
Addition- a+0=a and 0+a=a... Multiplication- a1=a 1a=a
Addition- a+b=b+a... Multiplication- ab=ba
Addition- (a+b)+c=a+(b+c)... Multiplication- (ab)c=a(bc)
Addition- the sum of another number and its opposite, or addi…
Identity Properties
Addition- a+0=a and 0+a=a... Multiplication- a1=a 1a=a
Commutative Properties
Addition- a+b=b+a... Multiplication- ab=ba
47 terms
Geometry Postulates, Theorem, Properties, and Definitions
Unit 1
Postulate 1.1
Postulate 1.2
Postulate 1.3
...
Any two points make up one line.
Two lines can only intersect at one point.
Two planes can only intersect through one line.
Unit 1
...
Postulate 1.1
Any two points make up one line.
30 terms
Geometry Postulates, Theorems, Definitions & Properties
Segment Addition Postualtes
Angle Addition Postulate
Linear Pair Theorem
Congruent Complements Theorem
If B is between A and C, the AB+BC=AC (part + part = whole)
If C is in the interior of ∠AOD, then m∠AOC + m∠COD = m∠AOD (…
if 2 ∠'s form a linear pair, then they are supplementary (180°)
If 2 ∠'s are complementary (90°) to the same ∠ or to ≅ ∠'s th…
Segment Addition Postualtes
If B is between A and C, the AB+BC=AC (part + part = whole)
Angle Addition Postulate
If C is in the interior of ∠AOD, then m∠AOC + m∠COD = m∠AOD (…
24 terms
Geometry: Definitions, Properties, Postulates, & Theorems
One line
One plane
By its three noncollinear points or by…
A line
Through any teo points there is exactly...
Through any three noncollinear points, there is exactly...
Name a plane
Contains at least two points
One line
Through any teo points there is exactly...
One plane
Through any three noncollinear points, there is exactly...
91 terms
Geometry: Definitions, Postulates/Properties, Theorems
Def of rt. <
Def of perpendicular
Def of congruent
Def of midpoint
m< = 90
_|_ = rt<
= - congruent
Midpoint -- 2 congruent parts
Def of rt. <
m< = 90
Def of perpendicular
_|_ = rt<
14 terms
Geometry postulates, definitions, properties, and theorems
Reflexive Property
Substitution Property
Transitive
Theorem 2-1
a = a
If a = b, then either a or b may be substituted for the other…
If a = b and b = c, then a = c
If M is the midpoint of AB, then AM = 1/2AB and MB = 1/2AB
Reflexive Property
a = a
Substitution Property
If a = b, then either a or b may be substituted for the other…
26 terms
Geometry: Properties, Definitions, Postulates, and Theorems
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If a=b, then a+b=b+c
If a=b, then a-c=b-c
If a=b, then ac=bc
If a=b, then a/c=b/c
Addition Property of Equality
If a=b, then a+b=b+c
Subtraction Property of Equality
If a=b, then a-c=b-c
18 terms
Geometry Definitions , Postulates, Properties and Theorems
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 =/, 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
27 terms
Geometry Definitions, Postulates, Properties and Theorems
Segment Addition Postulate
Angle Addition Postulate
Linear Pair Property
Addition Property of Equality
If point B is between A and C on a line, then AB+BC=AC
If D is in the interior of <ABC then: m<ABD+m<DBC=m<ABC
If two <'s form a straight line, then they are supplementary
x-4=11 ... x=15
Segment Addition Postulate
If point B is between A and C on a line, then AB+BC=AC
Angle Addition Postulate
If D is in the interior of <ABC then: m<ABD+m<DBC=m<ABC
77 terms
Geometry Definitions, Theorems, Properties, and Postulates
Collinear Points
Noncollinear Points
Line Postulate
Plane Postulate
Points that lie on the same line.
Points that do not lie on the same line.
Two points determine a unique straight line.
Three noncollinear points determine a unique plane.
Collinear Points
Points that lie on the same line.
Noncollinear Points
Points that do not lie on the same line.
34 terms
Postulates, Theorems, Definitions, and Properties~Geometry
def. supplementary
def. supplementary
def. complementary
def. right angle
m<1+m<2=180... <1 supp <2
<A supp <B... m<A + m<B =180
<1 comp <2... m<1 + m<2=90
<ABC is a rt <... m<ABC=90
def. supplementary
m<1+m<2=180... <1 supp <2
def. supplementary
<A supp <B... m<A + m<B =180
59 terms
Geometry: Postulates, Properties, Theorems, and Definitions
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…
30 terms
Geometry (Definitions, Properties, Postulates, Theorems)
Angle Addition Postulate
Corresponding Angles Postulate
Parallel Postulate
Coplanar
If a point lies on the interior of an angle, that angle is th…
If a transversal intersects two parallel lines, the pairs of…
Given a line and a point not on that line, there exists a uni…
Two lines that are on the same plane
Angle Addition Postulate
If a point lies on the interior of an angle, that angle is th…
Corresponding Angles Postulate
If a transversal intersects two parallel lines, the pairs of…
62 terms
Geometry Properties, Postulates, Theorems and Definitions
Def RT
Def perpendicular
Law of detachment
Law of contrapositive
Right angles are 90 degrees
a straight line at an angle of 90
If p->q then Q must be true
If p ->q then ~Q -> ~P must be true
Def RT
Right angles are 90 degrees
Def perpendicular
a straight line at an angle of 90
15 terms
Geometry Definitions, Properties, Postulates, and Theorems
definition of perpendicular lines
addition property
subtraction property
multiplication property
if 2 lines intersect to form a right angle, then they are per…
if a = b, then a + c = b + c
if a = b, then a - c = b - c
if a = b, then ac = bc
definition of perpendicular lines
if 2 lines intersect to form a right angle, then they are per…
addition property
if a = b, then a + c = b + c
27 terms
Geometry Theorems, postulates, definitions, and properties
Addition property
Subtraction property
Multiplication property
Division property
a=b and c=d, then a+c = b+d
a=b and c=d, then a-c = b-d
a=b, then ca = cb
a=b, then a/c = b/c where C doesn't = 0
Addition property
a=b and c=d, then a+c = b+d
Subtraction property
a=b and c=d, then a-c = b-d
27 terms
Geometry definitions, theorems, postulates, and properties
Vertical angles
Angle bisector
Segment bisector
Midpoint
Two angles whose sides form two pairs of opposite rays
A ray that divides an angle into two adjacent angles that are…
A segment, Ray, line, or plane that intersects a segment at i…
The point that divides, or bisects a segment into 2 congruent…
Vertical angles
Two angles whose sides form two pairs of opposite rays
Angle bisector
A ray that divides an angle into two adjacent angles that are…
16 terms
Geometry Definitions, Postulates, Properties, and Theorems
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 is not equal to 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
57 terms
Geometry theorems, postulates, definitions, and properties.
Definition 1
Definition 2
Postulate 1
Postulate 2
Collinear Points are points are points that lie on the same l…
Noncollinear points are points that do not lie on the same li…
Two points determine a unique straight line.
Three noncollinear points determine a unique plane.
Definition 1
Collinear Points are points are points that lie on the same l…
Definition 2
Noncollinear points are points that do not lie on the same li…
8 terms
Geometry definitions, theorems, postulates and properties
Definition of congruence
Segment Addition Postulate
Transitive property
Symmetric property of Equality
If AB=CD then line segment AB is congruent to line segment CD
AB+BC=AC
if AB=CD and CD=EF then AB=EF
if AB=CD then CD=AB
Definition of congruence
If AB=CD then line segment AB is congruent to line segment CD
Segment Addition Postulate
AB+BC=AC
26 terms
Geometry Definitions, Properties, Postulates, and Theorems
Addition Property
Subtraction Property
Multiplication Property
Division Property
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
If a = b, then a + c = b + c.
Subtraction Property
If a = b, then a - c = b - c.
28 terms
Geometry Postulates, Theorems, Properties and Definitions
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 a x c=b x c
If a=b, then a/b=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
27 terms
Geometry: Properties, Postulates, Theorems and Definitions
Addition Property
Subtraction Property
Multiplication Property
Division Property
If 3=x, 3+2= x+2
If 3= x, 3-1 = x-1
If 5=m, then 4 (5) = 4m
If 20-5m, then 4 = m
Addition Property
If 3=x, 3+2= x+2
Subtraction Property
If 3= x, 3-1 = x-1
12 terms
Geometry: Properties, Postulates, Theorems, and Definitions
Addition Prop.
Subtraction Prop.
Multiplication Prop.
Division Prop.
If x = 7, then x + 3 = 10
If x = 10, then x - 3 = 7
If x = 2, then 2x = 4
If 2x = 4, then x = 2
Addition Prop.
If x = 7, then x + 3 = 10
Subtraction Prop.
If x = 10, then x - 3 = 7
29 terms
Geometry- Definitions, Properties, Theorems, & Postulates
If S isn in the interior of ∠PQR... Then…
If JK (ray) bisects ∠LJM... Then ∠LJK≅ ∠KJM
If ∠APC = ∠BPC... Then AC = BC
If two angle measures have a sum of 90…
Angle addition postulate
Definition of angle bisector
Angle bisector theorem
Definition of complimentary angles
If S isn in the interior of ∠PQR... Then…
Angle addition postulate
If JK (ray) bisects ∠LJM... Then ∠LJK≅ ∠KJM
Definition of angle bisector
23 terms
Geometry definitions, theorems, postulates, properties
Midpoint of a segment
Bisector of an angle
Complementary angles
Supplementary angles
the point that divides the segment into two congruent segments
line, ray, or segment that divides the angle into two congrue…
two angles whose sum is 90 degrees
two angles whose sum is 180 degrees
Midpoint of a segment
the point that divides the segment into two congruent segments
Bisector of an angle
line, ray, or segment that divides the angle into two congrue…
20 terms
Geometry Definitions, Postulates, Properties, & Theorems
Definition of congruent segments
Definition of congruent angles
Definition of right angle
Definition of linear pair
1. If segments are congruent, then they have the same measure…
1. If angles are congruent, then they have the same measure.…
1. If an angle has a measure of 90 degrees, then it is a righ…
1. If angles are adjacent angles and are formed by opposite r…
Definition of congruent segments
1. If segments are congruent, then they have the same measure…
Definition of congruent angles
1. If angles are congruent, then they have the same measure.…
19 terms
Geometry Definitions, Postulates, Properties, & Theorems
Definition of congruent segs/∠s
Definition of right angle
Definition of perpendicular
Definition of bisect
1. If segs/∠s are ≅, then segs/∠s have the same measure.... 2. I…
1. If ∠ is 90°, then ∠ is a rt. ∠.... 2. If ∠ is a rt. ∠, then ∠…
1. If lines form rt. ∠s, then they are ⊥.... 2. If lines are ⊥,…
1. If seg/∠ is bisected, then seg/∠ is div. into two ≅ parts.…
Definition of congruent segs/∠s
1. If segs/∠s are ≅, then segs/∠s have the same measure.... 2. I…
Definition of right angle
1. If ∠ is 90°, then ∠ is a rt. ∠.... 2. If ∠ is a rt. ∠, then ∠…
33 terms
Geometry Chapter 2 Properties, Definitions, Postulates, and Theorems
definition of congruent segments
definition of congruent angles
definition of right angles
definition of midpoint
Angle ABC is a right angle... The measure of angle ABC = 90 degr…
definition of congruent segments
definition of congruent angles
31 terms
Geometry Theorems, Postulates, and Properties
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.
Definitions, Properties, Postulates and Theorems
Segment Addition Postulate
Angle Addition Postulate
Definition of a Midpoint
Definition of a Right Angle
If B is between A and C then AB + BC = AC.
If S is inside of PQR then PQS + SQR = PQR
If the point is a midpoint then it bisects a segment (Two con…
If an angle is a right angle then the angle's measure is 90 d…
Segment Addition Postulate
If B is between A and C then AB + BC = AC.
Angle Addition Postulate
If S is inside of PQR then PQS + SQR = PQR
40 terms
Geometry Theorems, Properties, and Postulates
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 (a)(c) = (b)(c)
If a = b, c not equal to "zero", 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
23 terms
Geometry Terms (properties, postulates, definitions and theorems)
Ruler Postulate
Segment Addition Postulate
Angle Addition Postulate
Protractor Postulate
Every point on a line can be paired with a real number. This…
If three points A, B, and c are collinear and B in between A…
If point B is in the interior of angle AOC, then the measurem…
Consider ray OB and a point A on one side of ray OB. Every ra…
Ruler Postulate
Every point on a line can be paired with a real number. This…
Segment Addition Postulate
If three points A, B, and c are collinear and B in between A…
20 terms
Geometry Definitions, Postulates and Theorems
Definition of Midpoint
Vertical Angles Theorem
Reflexive property
Symmetric property
(Not def. Of congruent segments)
∠CXE=∠CXE
GH = KL so ... KL = GH
Definition of Midpoint
(Not def. Of congruent segments)
Vertical Angles Theorem
33 terms
Geometry Chapter 2 Properties, Definitions, Postulates, and Theorems
definition of congruent segments
definition of congruent angles
definition of right angles
definition of midpoint
Angle ABC is a right angle... The measure of angle ABC = 90 degr…
definition of congruent segments
definition of congruent angles
25 terms
Geometry Properties, Postulates, and Theorems
coordinate midpoint property
segment additive property
angle addition property
linear pair theorem
if B is between A & C,... then AB+BC=AC
if D is on the interior of Angle ABC,... then m Angle ABD + m An…
if two angles form a linear pair,... then the two angles are sup…
coordinate midpoint property
segment additive property
if B is between A & C,... then AB+BC=AC
33 terms
Geometry Chapter 2 Properties, Definitions, Postulates, and Theorems
definition of congruent segments
definition of congruent angles
definition of right angles
definition of midpoint
Angle ABC is a right angle... The measure of angle ABC = 90 degr…
definition of congruent segments
definition of congruent angles
35 terms
Geometry Theorems, Postulates, and Properties
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 a•c=b•c
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
142 terms
Geometry- All Definitions, Postulates, Theorems and Other properties
equidistant
point
line
plane
equally distant to the same point
an undefined term; location in space; no size
an undefined term; extends in 2 directions never ending; no s…
an undefined term; extends without ending; no thickness; need…
equidistant
equally distant to the same point
point
an undefined term; location in space; no size
59 terms
Geometry Postulates, Theorems, and Properties
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.
33 terms
Geometry Theorems, Definitions, Postulates, and Properties for Proofs
additive property
definition of a midpoint
definition of a circle
definition of equilateral triangle
if B is on segment AC, then AB + BC = AC
the midpoint of a segment AB is the point M on segment AB wit…
the set of all points in a plane at a certain positive distan…
has 3 sides of equal length (is also isosceles)
additive property
if B is on segment AC, then AB + BC = AC
definition of a midpoint
the midpoint of a segment AB is the point M on segment AB wit…
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