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Study sets matching "geometry proofs postulates theorems"

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Study sets matching "geometry proofs postulates theorems"

38 terms
Theorems and Postulates for Geometry Proofs
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
45 terms
Postulates & Theorems for Proofs (Geometry)
segment addition postulate (SAP)
angle addition postulate (AAP)
addition property of equality
subtraction property of equality
if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…
Angles can be added together if they are adjacent
Adding a value to each side of an equation... if a=b, then a+c=b+c
subtracting a value from each side of an equation ... if a=b the…
segment addition postulate (SAP)
if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…
angle addition postulate (AAP)
Angles can be added together if they are adjacent
9 terms
Geometry Postulates, Proofs, & 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, then a/c=b/c c is ALMOST equal to
Addition Property of Equality
if a=b, then a+c=b+c
Subtraction Property of Equality
if a=b, then a-c=b-c
41 terms
Geometry Proofs, Postulates, and Theorems
If B is between A & C then AB + BC =AC
If two angles have the same measuremen…
If the angles are congruent two angles…
If a point, X, is in the interior of <…
segment addition postulate
definition of congruent angles
definition of congruent angles
angle addition postulate
If B is between A & C then AB + BC =AC
segment addition postulate
If two angles have the same measuremen…
definition of congruent angles
43 terms
Geometry Proofs - Postulates and Theorems
Segment Addition postulate
Angle Addition postulate
Linear Pair postulate
Definition of Congruence
If M is between A and B, then AM+MB=AB.
If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.
If two angles form a linear paire, then they are supplementary.
If measures are equal, then parts are congruent.
Segment Addition postulate
If M is between A and B, then AM+MB=AB.
Angle Addition postulate
If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.
38 terms
Geometry Postulates, Proofs, and Theorems
Ruler Postulate
Segment Addition Postulate
Protector Postulate
Angle Addition Postulate
AB = distance between endpoints
AB+BC=AC if B is between A and C
Ruler Postulate for Angles
Segment Addition Postulate for Angles
Ruler Postulate
AB = distance between endpoints
Segment Addition Postulate
AB+BC=AC if B is between A and C
22 terms
Postulates, Theorems, Proofs - Geometry
Ruler Postulate
Segment Addition Postulate
Postulate
Protractor 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.
A rule accepted without proof
An angle can be measured from 0 to 180
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.
34 terms
Geometry proofs - postulates/theorems
segment addition postulate
Def: Midpoint of a segment
Def: Bisector of a segment
angle addition postulate
if B is between A and C, then AB + BC = AC
The point that divides the segment into two congruent segments
A line, segment, ray, or plane that intersects the segment at…
If point B lies in the interior of <AOC, then m<AOB + m<BOC =…
segment addition postulate
if B is between A and C, then AB + BC = AC
Def: Midpoint of a segment
The point that divides the segment into two congruent segments
21 terms
geometry theorems, proofs, postulate
segment addition postulate
reflexive property of congruence
symmetric property of congruence
Transitive property of congruence
if A,B, and C are collinear, then point B is between A and C…
segment AB is congruent to segment AB
if segment AB is congruent to segment CD, the segment CD is c…
if segment AB is congruent to segment CD and CD is congruent…
segment addition postulate
if A,B, and C are collinear, then point B is between A and C…
reflexive property of congruence
segment AB is congruent to segment AB
8 terms
Postulates and Theorems Geometry Proofs
Ruler Postulate
Protractor Postulate
Angle Addition Postulate
Segment Addition Postulate
On a number line, every point can be paired with a number and…
Given line AB and a point O on line AB. Consider rays OA and…
The angle addition postulate states that if B is in the inter…
If a point B lies on a line segment , then . That is, the dis…
Ruler Postulate
On a number line, every point can be paired with a number and…
Protractor Postulate
Given line AB and a point O on line AB. Consider rays OA and…
25 terms
Geometry Theorems Postulates and Proofs
Slopes of parallel lines
Parallel Postulate
Slopes of Perpendicular Lines
Symmetric Property
If 2 nonvertical lines are parallel then their slopes are equ…
Through a point not on a line, there is ONLY ONE parallel to…
If 2 nonvertical lines are perpendicular, then the product of…
If a=b then b=a
Slopes of parallel lines
If 2 nonvertical lines are parallel then their slopes are equ…
Parallel Postulate
Through a point not on a line, there is ONLY ONE parallel to…
33 terms
Geometry Proofs Theorems and postulates
Triangle Angle-Sum Theorem
Exterior angle Theorem
Triangle Angle Sum Corollaries
Definition of Congruent Polygons
The sum of the measures of the angles of a triangle is 180
The measure of an exterior angle of a triangle is equal to th…
The acute angles of a right triangle are complementary... There…
Two polygons are congruent if and only if their corresponding…
Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180
Exterior angle Theorem
The measure of an exterior angle of a triangle is equal to th…
39 terms
Geometry Proofs, postulates, and Theorems
Postulate or axion
Postulate 2.1
Postulate 2.2
Postulate 2.3
A statement that is accepted as true without proof
Through any two distinct points there exists only 1 line
Though any 2 distinct points there exists exactly 1 plane
A line contains at least 2 points
Postulate or axion
A statement that is accepted as true without proof
Postulate 2.1
Through any two distinct points there exists only 1 line
44 terms
Geometry PROOFS: Theorems and Postulates
Segment Addition Postulate (SAP)
VAT
Linear Pair Thm
AAP
AB + BC = AC
Two angles are vertical iff their sides form opposite rays
Two adjacent angles form a linear pair iff their non-common s…
Angle Addition Postulate states that if a point S lies in the…
Segment Addition Postulate (SAP)
AB + BC = AC
VAT
Two angles are vertical iff their sides form opposite rays
27 terms
GEOMETRY PROOFS POSTULATES AND THEOREMS
Alternate Interior Angles Theorem
Same Side Interior Angles Theorem
Alternate Exterior Angles Theorem
Same Side Exterior Angles Theorem
If 2 parallel lines are intersected by a transversal, then al…
If 2 parallel lines are cut by a transversal, then same side…
If 2 parallel lines are cut by a transversal, the alternate e…
If 2 parallel lines are are cut by a transversal, the same si…
Alternate Interior Angles Theorem
If 2 parallel lines are intersected by a transversal, then al…
Same Side Interior Angles Theorem
If 2 parallel lines are cut by a transversal, then same side…
45 terms
Postulates & Theorems for Proofs (Geometry)
segment addition postulate (SAP)
angle addition postulate (AAP)
addition property of equality
subtraction property of equality
if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…
Angles can be added together if they are adjacent
Adding a value to each side of an equation... if a=b, then a+c=b+c
subtracting a value from each side of an equation ... if a=b the…
segment addition postulate (SAP)
if B is between A and C, then AB + BC = AC... if AB + BC = AC, t…
angle addition postulate (AAP)
Angles can be added together if they are adjacent
5 terms
Geometry Theorems, Postulates, and Proofs
Conditional Statement
Converse
Inverse
Contraposistive
A logical statement that has two parts; a hypothesis, and a c…
A conditional statement that switches the places of the hypot…
When the hypothesis and conclusion of a conditional statement…
When the hypothesis and conclusion of a conditional statement…
Conditional Statement
A logical statement that has two parts; a hypothesis, and a c…
Converse
A conditional statement that switches the places of the hypot…
43 terms
Geometry Proofs - Postulates and Theorems
Segment Addition postulate
Angle Addition postulate
Linear Pair postulate
Definition of Congruence
If M is between A and B, then AM+MB=AB.
If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.
If two angles form a linear paire, then they are supplementary.
If measures are equal, then parts are congruent.
Segment Addition postulate
If M is between A and B, then AM+MB=AB.
Angle Addition postulate
If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.
15 terms
Geometry Proofs, Theorems, and Postulates
Corresponding Angle Postulate
Alternate Interior Angle Postulate
Alternate Exterior Angle Postulate
Same-Side Consecutive Interior Angles…
If 2 // lines are cut by a transversal then the corresponding…
If 2 // lines are cut by a transversal then all alternate int…
If 2 angles are cut by a transversal then all alternate exter…
If 2 parallel lines are cut by a transversal then same side i…
Corresponding Angle Postulate
If 2 // lines are cut by a transversal then the corresponding…
Alternate Interior Angle Postulate
If 2 // lines are cut by a transversal then all alternate int…
25 terms
geometry: proof theorems and postulates
adjacent angles
liner pair
vertical angle
addition property of equality
share a common side and vertex
two adjacent angles that have a non common side and forms a l…
two non adjacent angles that are formed by two intersecting l…
if a, b and c are real numbers and a=b the a+c = b+c
adjacent angles
share a common side and vertex
liner pair
two adjacent angles that have a non common side and forms a l…
31 terms
Geometry Postulate, Proofs, and Theorems
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
For every two points there is one line
Brought every three non collinear points there is one plane
For every line there are at least two points
Through every plain there are at least three points
Postulate 2.1
For every two points there is one line
Postulate 2.2
Brought every three non collinear points there is one plane
16 terms
Geometry postulates, theorems and proof
What is a postulate
Postulate: through any two points
Postulate: through any three no collin…
Postulate: two lines intersect in a
A statement that is accepted as true without proof
There is exactly one line
There is exactly one plane
Point (vertex)
What is a postulate
A statement that is accepted as true without proof
Postulate: through any two points
There is exactly one line
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
16 terms
Geometry Theorems/Postulates/Properties for PROOFS
AB = AB
BC = CB
If A = B, and B = C, then A = C
If two lines are perpendicular, then y…
Reflexive Property
Symmetric Property
Transitive Property
Definition of Perpendicular Lines
AB = AB
Reflexive Property
BC = CB
Symmetric Property
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
20 terms
Geometry Properties, Postulates, and Theorems for Proofs
transitive property of equality
reflexive property of equality
the angle addition postulate
supplement postulate
If a = b and b = c, then a = c
a = a
Postulate 13: If D is in the interior of angle BAC, then the…
Postulate 14: If two angles form a linear pair, then they are…
transitive property of equality
If a = b and b = c, then a = c
reflexive property of equality
a = a
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
Commutative Property of Addition
a + b = b +a
Commutative Property of Multiplication
ab = ba
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
9 terms
Geometry Proofs- Theorems, Postulates, and Definitions
Alternate Exterior Angle Theorem
Corresponding Angle Postulate
Alternate Interior Angle Theorem
Same Side (Consecutive) Interior Angle…
If 2 parallel lines are cut by a transversal, then alternate…
If 2 parallel lines are cut by a transversal, then correspond…
If two parallel lines are cut by a transversal, then alternat…
If two parallel lines are cut by a transversal, then same sid…
Alternate Exterior Angle Theorem
If 2 parallel lines are cut by a transversal, then alternate…
Corresponding Angle Postulate
If 2 parallel lines are cut by a transversal, then correspond…
25 terms
Definitions, Postulates, and Theorems for Geometry Proofs
def. of ≅ ∠s
def. of ∠ bisector
∠ bisector theorem
transitive property of ≅
use when you change from ≅ ∠s to = measures and vice versa
if BD bisects ∠ABC, then ∠ABD ≅ ∠DBC
if AD bisects ∠ABC, m∠ABD = (1/2)m∠ABC
If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3
def. of ≅ ∠s
use when you change from ≅ ∠s to = measures and vice versa
def. of ∠ bisector
if BD bisects ∠ABC, then ∠ABD ≅ ∠DBC
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
38 terms
Geometry Theorems, Postulates, And Definitions for Proofs
Theorem 4.1
Theorem 4.2
Theorem 4.3
Theorem 4.4
All right angles are congruent
If two angles are adjacent and supplementary, then they form…
Angles that form a linear pair are supplementary
If one angle of a linear pair is right, then the other angle…
Theorem 4.1
All right angles are congruent
Theorem 4.2
If two angles are adjacent and supplementary, then they form…
18 terms
Geometry Properties, Postulates, and Theorems for Proofs
distributive property
addition property of equality
subtraction property of equality
multiplication property of equality
a(b + c) = ab + ac
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 and c = d, then ac = bd
distributive property
a(b + c) = ab + ac
addition property of equality
If a = b and c = d, then a + c = b + d
33 terms
Geometry Proofs/Postulates/Theorems/Properties
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
Through any 2 points there is exactly one line
Through any 3 noncollinear points, there is exactly one plane
A line contains at least 2 points
A plane contains at least 3 noncollinear points
Postulate 2.1
Through any 2 points there is exactly one line
Postulate 2.2
Through any 3 noncollinear points, there is exactly one plane
24 terms
geometry proofs- postulates, theorems, and definitions
right angle theorem (1)
theorem 2
theorem 3
postulate 1
If two angles are right angles, then they are congruent
If two angles are right angles, then they are congruent
If a conditional statement is true, then the contrapositive i…
Segment Addition (can be used as Angle Addition) - as we prac…
right angle theorem (1)
If two angles are right angles, then they are congruent
theorem 2
If two angles are right angles, then they are congruent
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
23 terms
Geometry - Proofs Algebraic/ Postulates/ and Theorems
What the Symbols Mean
Linear Pair Theorem
Congruent Supplements Theorem
Right Angles Congruent Theorem
{=} - means that it is Congruent... * - is the symbol for degrees
If two angles form a linear pair, then they are supplementary
If two angles are supplementary to the same right angle(or to…
All right angles are congruent
What the Symbols Mean
{=} - means that it is Congruent... * - is the symbol for degrees
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
24 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
19 terms
Geometry Proof Postulates, Properties, & Theorems
Addition Property (Equality)
Subtraction Property (Equality)
Multiplication Property (Equality)
Division Property (Equality)
If the same number is added to equal numbers, then the sums a…
If the same number is subtracted from equal numbers, then the…
If the equal numbers are multiplied by the same number, then…
If equal numbers are divided by the same... number, then the quo…
Addition Property (Equality)
If the same number is added to equal numbers, then the sums a…
Subtraction Property (Equality)
If the same number is subtracted from equal numbers, then the…
14 terms
Theorems, Definitions and Postulates for Proofs (Geometry)
Additive Property
Definition of an Equilateral Triangle
Definition of Complimentary Angles
Definition of Supplementary Angles
If B is on line AC, then AB+BC=AC
If a figure is an isosceles triangle, then it has at least tw…
If two angles are complimentary, then the sum of their angles…
If two angles are supplementary, then the sum of their angles…
Additive Property
If B is on line AC, then AB+BC=AC
Definition of an Equilateral Triangle
If a figure is an isosceles triangle, then it has at least tw…
39 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
51 terms
Geometry Postulates, Properties and Theorems - Proofs
Through any two points, there is exact…
Through any three noncollinear points,…
A line contains at least two points (p…
A plane contains at least three non co…
What do two points make up?
What do three points make up?
How many points does a line contain
How many points does a plane contain
Through any two points, there is exact…
What do two points make up?
Through any three noncollinear points,…
What do three points make up?
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
41 terms
Geometry Properties, Postulates, and Theorems for Proofs
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication
a + b = b +a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
commutative property of addition
a + b = b +a
commutative property of multiplication
ab = ba
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