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Study sets matching "postulates geometry theorems"

21 terms
Geometry I Postulates and Theorems
Through any two points there is exactl…
Through any three points there is at l…
If two lines intersect, then they inte…
If two planes intersect, then their in…
...
...
...
...
Through any two points there is exactl…
...
Through any three points there is at l…
...
62 terms
Geometry Postulates and Theorems
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
64 terms
Geometry Postulates and Theorems
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
37 terms
Geometry Postulates and Theorems
Diagonals of a Rectangle Theorem
Diagonals of a Rhombus Theorem
Bisecting Diagonals of a Rhombus Theorem
Midpoint of a Hypotenuse Theorem
The diagonals of a retangle are congruent.
The diagonals of a rhombus are perpendicular.
Each diagonal of a rhombus bisects the two angles of the rhom…
The midpoint of the hypotenuse of a right triangle is equidis…
Diagonals of a Rectangle Theorem
The diagonals of a retangle are congruent.
Diagonals of a Rhombus Theorem
The diagonals of a rhombus are perpendicular.
58 terms
Geometry Postulates, Theorems, and Definitions
Definition
Postulate
Theorem
Line Segment
a list of properties an object must have
a basic assumption
a statement that has been proven true
two points on a line and all points that lie between them
Definition
a list of properties an object must have
Postulate
a basic assumption
9 terms
geometry postulates/theorems
Line tangent to circle→Line perpendicu…
Line perpendicular to radius→line tang…
2 segments tangent to circle from same…
Arc addition postulate
If a line is tangent to a circle, then the line is perpendicu…
If a line is perpendicular to the radius, then it is tangent…
If two segments are tangent to a circle from the same externa…
the measure of an arc formed by two adjacent arcs is the sum…
Line tangent to circle→Line perpendicu…
If a line is tangent to a circle, then the line is perpendicu…
Line perpendicular to radius→line tang…
If a line is perpendicular to the radius, then it is tangent…
18 terms
Geometry Theorems and Postulates
Area Formula for a Triangle in terms o…
Law of Sines
Law of Cos
Arc Addition Postulate
area= 1/2 x side1 x side2 x sin(included angle)
Sin(A)/a=Sin(B)/b=Sin(C)/c
a^2=b^2+c^2-2(bc)Cos(A)... b^2=a^2+c^2-2(ac)Cos(B)... c^2=a^2+b^2-2…
The measure of an arc formed by 2 adjacent arcs is the sum of…
Area Formula for a Triangle in terms o…
area= 1/2 x side1 x side2 x sin(included angle)
Law of Sines
Sin(A)/a=Sin(B)/b=Sin(C)/c
22 terms
Geometry Theorems and Postulates
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.... If AB + BC = AC,…
Consider ray OB and a point A on one side of ray OB .... The ray…
Words If P is in the interior of ∠ RST, then the measure of ∠…
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.... If AB + BC = AC,…
31 terms
Geometry Honors Postulates and Theorems
Postulate 1-1-1
Postulate 1-1-2
Postulate 1-1-3
Postulate 1-1-4
Through any two points there is exactly one line
Through any three noncollinear points there is exactly one pl…
If two points lie in a plane, then the line containing those…
If two lines intersect, then they intersect in exactly one po…
Postulate 1-1-1
Through any two points there is exactly one line
Postulate 1-1-2
Through any three noncollinear points there is exactly one pl…
8 terms
Geometry Unit 2 Theorems and Postulates
Law Of Detachment
Law Of Syllogism
Linear Pair Theorem
Congruent Supplements Theorem
If P>Q is a true statement and P is true, then Q is true
If P>Q and Q>R are true statements, then P>R is a true statem…
If two angles form a linear pair, then they are supplementary…
If two angles are supplementary to the same angle, then the t…
Law Of Detachment
If P>Q is a true statement and P is true, then Q is true
Law Of Syllogism
If P>Q and Q>R are true statements, then P>R is a true statem…
83 terms
Geometry Theorems, Postulates, and Corollaries
Corollaries
Corollaries
Corollaries
Supplementary Angle Theorem
If two angles of one triangle are congruent to two angles of…
Each angle of an equiangular triangle measures sixty degrees
In a triangle there can be at most one right angle or one obt…
All angles which are supplementy to the same or equal angles…
Corollaries
If two angles of one triangle are congruent to two angles of…
Corollaries
Each angle of an equiangular triangle measures sixty degrees
72 terms
Geometry Postulates, Theorems, and Definitons
segment addition postulate (1.2)
midpoint (1.3)
segment bisector (1.3)
angle addition postulate (1.5)
when 3 points are collinear, you can say that one point is be…
midpoint of a segment is the point that divides the segment i…
point, ray line, line segment or plane that intersects the se…
if angle AB is equal to angle BC, then angle AB + angle BC = AC
segment addition postulate (1.2)
when 3 points are collinear, you can say that one point is be…
midpoint (1.3)
midpoint of a segment is the point that divides the segment i…
128 terms
Geometry- Postulates, Theorems, Definitions Etc
undefined term
point
line
plane
a word without a formal definition
undefined, a location with no size or dimension
undefined, a series of infinite points that extends in two di…
undefined, flat surface that has no thickness and extends in…
undefined term
a word without a formal definition
point
undefined, a location with no size or dimension
48 terms
Honors Geometry Postulates and Theorems
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on a line can be matched one to one with real numb…
If B is between A and C, then AB+BC=AC
Consider OB and a point A on one side of OB. The rays of the…
If P is the interior of angleRST, then the measure of angleRS…
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
21 terms
Geometry Postulates and Theorems (Chapter 2)
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 p…
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 p…
18 terms
Postulates, Propertys, and theorems- Geometry
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 does not equal 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
25 terms
Geometry Postulates, Theorems, and Rules
Ruler postulate
Segment addition postulate
Protractor postulate
Angle addition postulate
the distance between A and B is the Absolute value of the dif…
If B is between A and C, then AB+BC=AC
The measure of angle ABC is equal to the absolute value of th…
If D is in the interior if angle ABC...... m<ABC=m<ABD+m<DBC
Ruler postulate
the distance between A and B is the Absolute value of the dif…
Segment addition postulate
If B is between A and C, then AB+BC=AC
Geometry Postulates and Theorems
there is exactly one line.
there is exactly one plane.
two points.
three noncollinear points.
Through any two points,
Through any three noncollinear points,
A line contains at least
A plane contains at least
there is exactly one line.
Through any two points,
there is exactly one plane.
Through any three noncollinear points,
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.
29 terms
Geometry Theorems, Postulates, and Properties
Segment Addition Postulate
Angle Addition Postulate
Two-Point Postulate
Line-Point Postulate
If B is between A and C, then AB+BC=AC.
If P is in the interior of ∠RST, then the measure of ∠RST is…
Through any two points, there is exactly one line.
A line contains at least two points.
Segment Addition Postulate
If B is between A and C, then AB+BC=AC.
Angle Addition Postulate
If P is in the interior of ∠RST, then the measure of ∠RST is…
27 terms
Geometry Theorems and Postulates Exam
Segment Addition Postulate
Angle Addition Postulate
Linear Pair Theorem
Right Angle Congruence Theorem (or Rig…
If B is between A and C, the AB + BC = AC.
If O is in the interior of <ABC, then m<ABO + m<OBC = m<ABC
If two angles form a linear pair, then they are supplementary…
All right angles are congruent.
Segment Addition Postulate
If B is between A and C, the AB + BC = AC.
Angle Addition Postulate
If O is in the interior of <ABC, then m<ABO + m<OBC = m<ABC
49 terms
Geometry-H Postulates and Theorems
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 ray AB in a given plane, choose any point O between A and…
If point B lies in the interior of <AOC, then... m< AOB + 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
50 terms
Geometry 280 Theorems and Postulates
angle addition postulate
segment addition postulate
linear pair postulate
corresponding angles postulate
if a point S lies in the interior of ∠PQR, then ∠PQS + ∠SQR =…
if point B is between points A and C, then AB + BC = AC
if two angles form a linear pair, then they are supplementary
if two parallel lines are cut by a transversal, then the pair…
angle addition postulate
if a point S lies in the interior of ∠PQR, then ∠PQS + ∠SQR =…
segment addition postulate
if point B is between points A and C, then AB + BC = AC
170 terms
GEOMETRY | THEOREMS, POSTULATES, AND FORMULAS
Surface Area
Lateral Area right prism
Volume of right prism
Lateral Area of regular pyramid
lateral area + 2B
Ph (Perimeter x height)
Bh (total area of Base x height)
1/2 P ℓ (ℓ = slant height)
Surface Area
lateral area + 2B
Lateral Area right prism
Ph (Perimeter x height)
33 terms
Geometry postulates, theorems, and formulas
Segment addition postulate
Midpoint formula
Distance formula
Postulate 5
if B is between A and C then AB+BC=AC
through any 2 points exists exactly 1 line
Segment addition postulate
if B is between A and C then AB+BC=AC
Midpoint formula
14 terms
Geometry Unit 3 Theorems And Postulates
Corresponding Angles Postulate
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
Same-Side Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the two…
If two parallel lines are cut by a transversal, then the two…
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pair…
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pair…
Triangles - Theorems and Postulates for Geometry
Side-Side-Side (SSS) Congruence
Side-Angle-Side (SAS) Congruence
Angle-Side-Angle (ASA) Congruence
Angle-Angle-Side (AAS) Congruence
If three sides of one triangle are congruent to three sides o…
If two sides and the included angle of one triangle are congr…
If two angles and the included side of one triangle are congr…
If two angles and the non-included side of one triangle are c…
Side-Side-Side (SSS) Congruence
If three sides of one triangle are congruent to three sides o…
Side-Angle-Side (SAS) Congruence
If two sides and the included angle of one triangle are congr…
18 terms
Geometry Theorem's/Postulates
Theorem 2-1: Vertical Angles Theorem
Theorem 2-2: Congruent Supplements The…
Theorem 2-3: Congruent Complements The…
Theorem 2-4
Vertical angles are always congruent.
If 2 angles are supplements of the same angle (or of congruen…
If 2 angles are complements of the same angle (or of congruen…
All right angles are congruent
Theorem 2-1: Vertical Angles Theorem
Vertical angles are always congruent.
Theorem 2-2: Congruent Supplements The…
If 2 angles are supplements of the same angle (or of congruen…
18 terms
Important Geometry Postulates and Theorems
distance formula
midpoint formula
right angle congruence theorem
congruent supplements theorem
all right angles are congruent
if two angles are supplementary to the same angle (or to cong…
distance formula
midpoint formula
47 terms
Saxon Geometry: Theorems and Postulates
Postulate 1: Ruler Postulate
Postulate 2: Segment Addition Postulate
Postulate 4: The Angle Addition Postul…
Postulate 5
The points on a line can be paired in a one-to-one correspond…
If B is between A and C, then AB + BC = AC
If point D is in the interior of angle ABC, then the m of ang…
Through any two points there is exactly one line.
Postulate 1: Ruler Postulate
The points on a line can be paired in a one-to-one correspond…
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Parallels- Theorems and Postulates for Geometry
Corresponding Angles
Corresponding Angles Converse
Alternate Interior Angles
Alternate Exterior Angles
If two parallel lines are cut by a transversal, then the pair…
If two lines are cut by a transversal and the corresponding a…
If two parallel lines are cut by a transversal, then the alte…
If two parallel lines are cut by a transversal, then the alte…
Corresponding Angles
If two parallel lines are cut by a transversal, then the pair…
Corresponding Angles Converse
If two lines are cut by a transversal and the corresponding 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
48 terms
Geometry Theorems, Postulates, and Formulas
midpoint formula
distance formula
corresponding angles
alternate interior angles
midpoint formula
distance formula
23 terms
Geometry EOC Theorems and Postulates
Midpoint Formula
The Distance Formula
The Pythagorean Theorem
45-45-90
Midpoint Formula
The Distance Formula
Quadrilaterals-Theorems and Postulates for Geometry
Parallelograms- About Sides
Parallelograms- About Angles
Parallelograms- About Diagonals
Parallelogram Converses- About Sides
If a quadrilateral is a parallelogram, the opposite... sides ar…
* If a quadrilateral is a parallelogram, the opposite... angles…
* If a quadrilateral is a parallelogram, the diagonals... bisec…
* If both pairs of opposite sides of a quadrilateral... are par…
Parallelograms- About Sides
If a quadrilateral is a parallelogram, the opposite... sides ar…
Parallelograms- About Angles
* If a quadrilateral is a parallelogram, the opposite... angles…
17 terms
Geometry Theorems, Postulates, and Corolaries
Addition property of inequality (≠)
multiplication and division property o…
transitive property of inequality (≠)
Property of inequality (≠)
If a > b and c > d, then a + c > b + d
If a > b and c > 0, then ac > bc and a/c > b/c;... If a > b and…
If a > b and b > c, then a > c
If a = b + c and c > 0, then a > b and a> c
Addition property of inequality (≠)
If a > b and c > d, then a + c > b + d
multiplication and division property o…
If a > b and c > 0, then ac > bc and a/c > b/c;... If a > b and…
33 terms
Geometry Postulates, Theorems, Definitions, etc.
Postulate 1 (Ruler Postulate)
Postulate 2 (Segment Addition Postulate)
Postulate 3 (Protractor Postulate)
Postulate 4 (Angle Addition Postulate)
The distance between points a and b is the absolute value of…
If B is in between A and C, then AB+BC=AC
The measure of angle AOB is equal to the absolute value of th…
If point B is in the interior of angle COA, then the measure…
Postulate 1 (Ruler Postulate)
The distance between points a and b is the absolute value of…
Postulate 2 (Segment Addition Postulate)
If B is in between A and C, then AB+BC=AC
36 terms
Geometry Midterm: Theorems and Postulates
segment addition postulate
angle addition postulate
linear pair postualte
reflexive property
if 3 points a, b, and c are colinear and b is between a and c…
if point b is interior of <aoc; then m<aob + m<boc = m<aoc
if two angles form a linear pair; they must be supplementary
a = a
segment addition postulate
if 3 points a, b, and c are colinear and b is between a and c…
angle addition postulate
if point b is interior of <aoc; then m<aob + m<boc = m<aoc
93 terms
GEOMETRY FORMULAS, THEOREMS, AND POSTULATES
Slope-Intercept Form of a line
Slope formula
Positive slope
Negative slope
Slope-Intercept Form of a line
Slope formula
43 terms
Postulates and Theorems- Geometry Final
Corresponding Angles Postulate
Alternate Interior Angles Theorem
Consecutive Interior Angles Theorem
Alternate Exterior Angles Theorem
When 2 lines are cut by a transversal, if the lines are paral…
When 2 lines are but by a transversal, if the lines are paral…
When 2 lines are cut by a transversal, if the lines are paral…
When 2 lines are cut by a transversal, if the lines are paral…
Corresponding Angles Postulate
When 2 lines are cut by a transversal, if the lines are paral…
Alternate Interior Angles Theorem
When 2 lines are but by a transversal, if the lines are paral…
69 terms
Geometry Final - theorems/postulates
exterior angle inequality theorem
statement
converse
inverse
the measure of an exterior angle of a triangle is greater in…
if p, then q
if q, then p
if not p, then not q
exterior angle inequality theorem
the measure of an exterior angle of a triangle is greater in…
statement
if p, then q
Geometry Theorems and Postulates
Postulate 1-1-1
Postulate 1-1-2
Postulate 1-1-3
Postulate 1-1-4
Through any two points there is exactly one line.
Through any non collinear points there is exactly one plane c…
If two points lie in a plane, then the line containing these…
If two lines intersect, then they intersect in exactly one pl…
Postulate 1-1-1
Through any two points there is exactly one line.
Postulate 1-1-2
Through any non collinear points there is exactly one plane c…
30 terms
Geometry Postulates and Theorems
Law of Detatchment
Law of Syllogism
Ruler Postulate
Segment Addition Postulate
if a conditional is true, and the hypothesis statement is tru…
conclusion that the first statement must be equal to the hypo…
every segment is measureable
pieces add together; parts add to a whole.
Law of Detatchment
if a conditional is true, and the hypothesis statement is tru…
Law of Syllogism
conclusion that the first statement must be equal to the hypo…
19 terms
Geometry Postulates/ Theorems
Postulate 1
Postulate 2
Postulate 3
Postulate 4
The points on a line can be paired with real numbers in such…
If B is between A and C then AB+BC= AC
When angles can be paired to numbers
When a new angle is added because of a new point
Postulate 1
The points on a line can be paired with real numbers in such…
Postulate 2
If B is between A and C then AB+BC= AC
36 terms
GEOMETRY POSTULATES AND THEOREMS
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 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 exac…
Through any 3 noncollinear points there is exactly one plane
Postulate 1-1
Through any two points there is exactly one line
Postulate 1-2
If two distinct lines intersect,then they intersect in exactl…
25 terms
2015 Geometry Properties, Postulates, 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≠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
10 terms
Geometry Postulates and Theorems
Postulate #1
Postulate #2
Postulate #3
Postulate #4
through any two points there is exactly one line
through any three noncollinear points there is exactly one pl…
if two points lie in a plane, then the line containing those…
if two lines intersect, then they intersect inn exactly one p…
Postulate #1
through any two points there is exactly one line
Postulate #2
through any three noncollinear points there is exactly one pl…
Geometry Postulates and Theorems
Reflexive Property
SSS
SAS
ASA
Any segment or angle is congruent to itself
if there exists a correspondence between the vertices of two…
if there exists a correspondence between the vertices of two…
if there exists a correspondence between the vertices of two…
Reflexive Property
Any segment or angle is congruent to itself
SSS
if there exists a correspondence between the vertices of two…
72 terms
Geometry Theorems, Definitions, and postulates
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
64 terms
Geometry Postulates/Theorems/Corollaries
Postulate 1.1
Postulate 1.2
Postulate 1.3
Postulate 1.4
Through any 2 points there is exactly one line.
If two lines intersect then they intersect at exactly one poi…
If two planes intersect then they intersect at exactly one li…
Through any 3 Non-Collinear points there is exactly one plane.
Postulate 1.1
Through any 2 points there is exactly one line.
Postulate 1.2
If two lines intersect then they intersect at exactly one poi…
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