Study sets matching "geometry postulates proofs"
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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
Ruler Postulate 1
Segment addition postulate 2
Protractor Postulate 3
Postulate 5
The points on a line can be matched one to one with the real n…
If B is between A and C, then AB + BC=AC then B is between A a…
ConsiderOB and a point A on one side of OB. The Rays of the fo…
Through any two points there exists exactly one line
Ruler Postulate 1
The points on a line can be matched one to one with the real n…
Segment addition postulate 2
If B is between A and C, then AB + BC=AC then B is between A a…
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
Through any 2 points is exactly 1 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 is exactly 1 line.
Postulate 2.2
Through any 3 noncollinear points, there is exactly one plane.
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on a line can be matched one to one with the real n…
If B is between A and C, then AB + BC = AC. If AB + BC = AC, t…
Consider ray OB and a point A on one side of of ray OB. The ra…
If P is in the interior of angle of RST, then the measure of a…
Ruler Postulate
The points on a line can be matched one to one with the real n…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC. If AB + BC = AC, t…
deff of parellelogram
property of parellelogram
property of parellelogram
property of parellelogram
a quad with 2 sets of // sides
opp sides congruent
opp angles congruent
same side angles are supplementary
deff of parellelogram
a quad with 2 sets of // sides
property of parellelogram
opp sides congruent
2.1
2.2
2.3
2.4
through any 2 points, there is exactly 1 line
through any 3 noncollinear points, there is exactly 1 plane
a line contains at least 2 points
a plane contains at least 3 noncollinear points
2.1
through any 2 points, there is exactly 1 line
2.2
through any 3 noncollinear points, there is exactly 1 plane
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
Vertical Angles Congruence Theorem
Linear Pair Postulate
Congruent Supplements Theorem
Congruent Complements Theorem
Vertical Angles are Congruent.
If two angles form a linear pair, then they are supplementary.
If two angles are supplementary to the same angle (or to congr…
If two angles are complementary to the same angle (or to congr…
Vertical Angles Congruence Theorem
Vertical Angles are Congruent.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality
if a=b then a+c= b+c... you can add something to both sides of an…
if a=b then a-c= b-c... you can subtract something from both side…
if a=b then a x c = b x c... you can multiply both sides of an eq…
if a=b then a/c= b/c... you can divide both side of an equation b…
addition property of equality
if a=b then a+c= b+c... you can add something to both sides of an…
subtraction property of equality
if a=b then a-c= b-c... you can subtract something from both side…
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, th…
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 then…
segment addition postulate (SAP)
if B is between A and C, then AB + BC = AC... if AB + BC = AC, th…
angle addition postulate (AAP)
Angles can be added together if they are adjacent
Postulate 2.1
Postulate 2.2
postulate 2.3
postulate 2.4
Through any two points, there is EXACTLY one line.
Through any three noncollinear points, there is exactly one pl…
A line contains at LEAST two points.
A plane contains at least three noncollinear points.
Postulate 2.1
Through any two points, there is EXACTLY one line.
Postulate 2.2
Through any three noncollinear points, there is exactly one pl…
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.
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
If B is between A & C then AB + BC =AC
If two angles have the same measurement…
If the angles are congruent two angles…
If a point, X, is in the interior of <A…
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 measurement…
definition of congruent angles
1-1
1-2
1-3
1-4
Through any two points there is exactly one line.
If two distinct lines intersect, then they intersect in exactl…
If two distinct planes intersect, then they intersect in exact…
Through any three non-collinear points there is exactly one pl…
1-1
Through any two points there is exactly one line.
1-2
If two distinct lines intersect, then they intersect in exactl…
2.1
2.2
2.3
2.4
Through any two points, there is exactly one line.
Through any three noncollinear points, there is exactly one pl…
A line contains at least two points.
A plane contains at least three noncollinear points
2.1
Through any two points, there is exactly one line.
2.2
Through any three noncollinear points, there is exactly one pl…
Parallel Postulate
Segment Addition Postulate
Angle Addition Postulate
Segment Addition Postulate
only one line can be drawn through a given point so that the l…
If B is between A and C, then AB+BC=AC
If R is in the interior of <PQS, then <PQR+<RQS=<PQS
Length of pieces of a segment sum to the total length
Parallel Postulate
only one line can be drawn through a given point so that the l…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
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
isosceles triangle thm
converse of the isosceles triangle thm
perpendicular bisector thm
angle side angle post (asa)
if two sides of a triangle are congruent, then the angles oppo…
if two angles of a triangle are congruent, then the sides oppo…
points on a perpendicular bisector of a segment are equidistan…
if two angles and the included side of the triangle are congru…
isosceles triangle thm
if two sides of a triangle are congruent, then the angles oppo…
converse of the isosceles triangle thm
if two angles of a triangle are congruent, then the sides oppo…
given- <1 and <2 are a linear pair ... <1…
given- p is parallel to q... prove- <1= <2
given- 1=3... prove- p11q
Given- <1 and <2 are complementary... prov…
1. <1 and <2 are a linear pair... <1 ~= <2 (GIVEN)... 2. <1 and <2…
1. p is parallel to q (GIVEN)... 2. <1 = <3 (CAP)... 3. 2=3 (VERTICA…
1. 1=3 (GIVEN)... 2. 1=2 (ALTERNATE EXTERIOR)... 3. 2=3 (LOS)... 4.. (A…
1. given... 2. <1+<2= 90 (DEFINITION OF COMPLEMENTARY ANGLES)... 3.…
given- <1 and <2 are a linear pair ... <1…
1. <1 and <2 are a linear pair... <1 ~= <2 (GIVEN)... 2. <1 and <2…
given- p is parallel to q... prove- <1= <2
1. p is parallel to q (GIVEN)... 2. <1 = <3 (CAP)... 3. 2=3 (VERTICA…
Postulates (axioms)
Theorems
Reflexive
Symmetric
statement that seems to "obvious" that we accept them without…
a statement that is provided by deductive reasoning
a quantity is equal to itself
if equal quantities are equal to the same quantity then they a…
Postulates (axioms)
statement that seems to "obvious" that we accept them without…
Theorems
a statement that is provided by deductive reasoning
Reflexive
Symmetric
Transitive
Substitution
a quantity is equal to itself
an equality maybe expressed in either order
if equal quantities are equal to the same quantity then they a…
a quantity may be substituted for its equal
Reflexive
a quantity is equal to itself
Symmetric
an equality maybe expressed in either order
Proof
Postulate
Inductive reasoning
Conjecture
A logical argument that shows a statement to be true
A rule that is ... excepted without proof
And argument that goes from a specific statement to a general…
A unproven statement that is based on observation
Proof
A logical argument that shows a statement to be true
Postulate
A rule that is ... excepted without proof
2.1
2.2
2.3
2.4
through any 2 points, there is exactly one line
through any 3 non collinear points, there is exactly one plane
a line contains at least 2 points
a plane contains at least 3 non collinear points
2.1
through any 2 points, there is exactly one line
2.2
through any 3 non collinear points, there is exactly one plane