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Study sets matching "postulates geometry math"

13 terms
All Math Postulates (Geometry)
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
SSS
SAS
ASA
Any segment or angle is congruent to i…
Reflexive
If there exists a correspondence betwe…
SSS
13 terms
Math (Geometry) Postulates
Regular Conditional
Converse
Inverse
Contrapositive
p -> q
q -> p
~p -> ~q
~q -> ~p
Regular Conditional
p -> q
Converse
q -> p
13 terms
Math (Geometry) Postulates
Regular Conditional
Converse
Inverse
Contrapositive
p -> q
q -> p
~p -> ~q
~q -> ~p
Regular Conditional
p -> q
Converse
q -> p
202 terms
Math Theorems, Postulates, and Definitions. (Geometry)
Point
Line
Segment
Ray
A dot represented by a letter.
Two points determine a line. A line is never ending.
Two points determine a segment. A segment has a definite end…
Two points determine a ray. A ray has one definite end and a…
Point
A dot represented by a letter.
Line
Two points determine a line. A line is never ending.
50 terms
Math Geometry Theorems, Postulates, and Definitions
Collinear Points
Noncollinear Points
Coplanar Points
Noncoplanar
Points that are all in one line
Points that are not in one line
Points that are in one plane
Points that are in multiple planes
Collinear Points
Points that are all in one line
Noncollinear Points
Points that are not in one line
29 terms
Math geometry theorems, definitions, and postulates
Def. of congruent
Def. of midpoint
Segment bisector
Def. of acute
When two angles or lines are equal size. ... Ex. If line AD=BC t…
Divides a segment into two congruent segments... Ex. If f is the…
Point, line, segment, Ray, or plane, that divides a segment i…
angle less than 90*
Def. of congruent
When two angles or lines are equal size. ... Ex. If line AD=BC t…
Def. of midpoint
Divides a segment into two congruent segments... Ex. If f is the…
9 terms
Big Ideas Math Geometry Chapter 6 Postulates, Properties, & Theorems
Lies, Rays, and Segments in Triangles
Perpendicular Bisector Theorem
Converse of the Perpendicular Bisector…
Angle Bisector Theorem
In a plane, if a point lies on the perpendicular bisector of…
In a plane, if a point is equidistant from the endpoints of a…
If a point lies on the bisector of an angle, then it is ... equi…
Lies, Rays, and Segments in Triangles
Perpendicular Bisector Theorem
In a plane, if a point lies on the perpendicular bisector of…
9 terms
Big Ideas Math Geometry Chapter 8 Postulates, Properties, & Theorems
Perimeters of Similar Polygons
Areas of Similar Polygons
Angle-Angle (AA) Similarity Theorem
Side-Side-Side (SSS) Similarity Theorem
If two polygons are similar, then the ratio of their perimete…
If two polygons are similar, then the ratio of their areas is…
If two angles of one triangle are... congruent to two angles of…
If the corresponding side lengths of... two triangles are propor…
Perimeters of Similar Polygons
If two polygons are similar, then the ratio of their perimete…
Areas of Similar Polygons
If two polygons are similar, then the ratio of their areas is…
24 terms
Big Ideas Math Geometry Chapter 7 Postulates, Properties, & Theorems
Classifications of Quadrilaterals
Polygon Interior Angles Theorem
Corollary to the Polygon Interior... Angl…
Polygon Exterior Angles Theorem
The sum of the measures of the interior angles of a convex n-…
The sum of the measures of the interior angles of a... quadrilat…
The sum of the measures of the exterior angles of a convex po…
Classifications of Quadrilaterals
Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n-…
32 terms
Big Ideas Math Geometry Chapters 1 & 2 Postulates, Properties, & Theorems
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 line OB and a point A on one side of line OB. The ra…
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,…
12 terms
Big Ideas Math Geometry Chapter 9 Postulates, Properties, & Theorems
Triangle Longer Side Theorem
Triangle Larger Angle Theorem
Triangle Inequality Theorem
Pythagorean Theorem
If one side of a triangle is longer than another side, then t…
If one angle of a triangle is larger than another angle, then…
The sum of the lengths of any two sides of a triangle is grea…
In a right triangle, the square of the length of the hypotenu…
Triangle Longer Side Theorem
If one side of a triangle is longer than another side, then t…
Triangle Larger Angle Theorem
If one angle of a triangle is larger than another angle, then…
14 terms
Big Ideas Math Geometry Chapter 5 Postulates, Properties, & Theorems
Triangle Sum Theorem
Exterior Angle Theorem
Corollary to the Triangle Sum Theorem
Properties of Triangle Congruence
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 acute angles of a right triangle are complementary.
Triangle congruence is reflexive, symmetric, and transitive.…
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…
26 terms
Math geometry theorems, definitions, and postulates
Def. of congruent
Def. of midpoint
Segment bisector
Def. of angle bisector
When two angles or lines are equal size. ... Ex. If line AD=BC t…
Divides a segment into two congruent segments... Ex. If f is the…
Point, line, segment, Ray, or plane, that divides a segment i…
Ray that divides an angle into two congruent adjacent angles…
Def. of congruent
When two angles or lines are equal size. ... Ex. If line AD=BC t…
Def. of midpoint
Divides a segment into two congruent segments... Ex. If f is the…
48 terms
Math: Geometry (Terms, Postulates, Theorems, etc.)
point
plane
line
collinear points
a location (undefined term)
a flat surface made up of points; has no depth and extends in…
made up of points and has no thickness or width (undefined te…
points on the same line
point
a location (undefined term)
plane
a flat surface made up of points; has no depth and extends in…
16 terms
Geometry Math Midterm Theorems and Postulates
Congruent Supplements Theorem
Vertical Angles Theorem
Alternate interior angles theorem
Alternate exterior angles theorem
If two angles are supplementary to the same angle (or to the…
Vertical angles are congruent.
If two parallel lines are cut by a transversal, then the alte…
If two parallel lines are cut by a transversal, then the alte…
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to the…
Vertical Angles Theorem
Vertical angles are congruent.
18 terms
Math Geometry Theorems, Postulates, and Defininitions
Linear pair
Angle bisector
Congruent angles
Congruent segments
Two adjacent angles that form online who's noncommon sides ar…
A line, ray, or segment that divides an angle into two adjace…
Angles that have the same measure
Segments that have the same length
Linear pair
Two adjacent angles that form online who's noncommon sides ar…
Angle bisector
A line, ray, or segment that divides an angle into two adjace…
22 terms
Big Ideas Math Geometry Chapter 10 Postulates, Properties, & Theorems
Tangent Line to a Circle Theorem
External Tangent Congruence Theorem
Arc Addition Postulate
Congruent Circles Theorem
In a plane, a line is tangent to a circle if and ony if the l…
Tangent segments from a common external point are conruent.
The measure of an arc formed by two adjacent arcs is the sum…
Two circles are congruent circles if and only if they have th…
Tangent Line to a Circle Theorem
In a plane, a line is tangent to a circle if and ony if the l…
External Tangent Congruence Theorem
Tangent segments from a common external point are conruent.
19 terms
Math Theorems, Postulate, etc. Geometry
Reflexive Property of Equality (Refl.…
Symmetric Property of Equality (Symm.…
Transitive Property of Equality (Trans…
Substitution Property of Equality (Sub…
a=a
If a=b, the b=a
If a=b and b=c, the a=c
If a=b, then a may be replaced by b in any equation or expres…
Reflexive Property of Equality (Refl.…
a=a
Symmetric Property of Equality (Symm.…
If a=b, the b=a
17 terms
Chapter 2 Math Theorems, Postulates and Definitions Geometry
Complementary Angles
Supplementary Angles
Adjacent Angles
Linear Pair of Angles
2 angles whose sum is always 90 degrees
2 angles whose sum is always 180 degrees
A pair of angles that share a common side, and have no common…
A pair of adjacent angles whose non-common sides form opposit…
Complementary Angles
2 angles whose sum is always 90 degrees
Supplementary Angles
2 angles whose sum is always 180 degrees
15 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
14 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
22 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
32 terms
Big Ideas Math Geometry Chapters 1 & 2 Postulates, Properties, & Theorems
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 line OB and a point A on one side of line OB. The ra…
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,…
22 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
10 terms
Geometry Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Given two points, there corresponds a unique positive number…
Given two rays, there corresponds a unique positive number ca…
Ruler Postulate
Given two points, there corresponds a unique positive number…
Segment Addition Postulate
14 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
14 terms
Geometry: Postulates
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…
14 terms
Geometry Postulates
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 & C, then AB + BC = AC
Consider Ray OB and a point A on one side of Ray OB. The rays…
If P is in the interior of <RST, then m<RST + m<RSP = m<PST
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A & C, then AB + BC = AC
5 terms
Geometry Postulates
Postulate 1
Postulate 2
The Ruler Postulate (Postulate 3)
The Protractor Postulate (Postulate 4)
Two points determine a unique straight line.
Three noncollinear points determine a unique plane
a. To every point on a line there corresponds exactly one rea…
a. The rays in a half rotation (180 degrees) can be numbered…
Postulate 1
Two points determine a unique straight line.
Postulate 2
Three noncollinear points determine a unique plane
8 terms
Geometry Postulates
Postulate(a statement that is accepted…
Postulate 2
Postulate 3, postulate 4
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
Please see the text book for diagram explanation
Through any two points there is exactly one line
Postulate(a statement that is accepted…
The points on a line can be paired in a one-to-one correspond…
Postulate 2
If B is between A and C, then AB+BC=AC
7 terms
Geometry - Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
accepted rule that a ruler can find a distance
if B is between A and C, then AB + BC = AC
the measure of an angle is equal to the absolute value of the…
if P is in the interior of the angle RST, then the measure of…
Ruler Postulate
accepted rule that a ruler can find a distance
Segment Addition Postulate
if B is between A and C, then AB + BC = AC
15 terms
Geometry postulates
ruler postulate
Segment Addition Postulate (Seg. Add.…
Protractor Postulate
Angle Addition Postulate
1.)points must be put on a number line... 2.)the distance betwee…
if B is between A and C, then AB+BC=AC (page 12 in book)
used to find the measure of an angle... 1.) take the absolute va…
m<AOB + m<BOC = m< AOC
ruler postulate
1.)points must be put on a number line... 2.)the distance betwee…
Segment Addition Postulate (Seg. Add.…
if B is between A and C, then AB+BC=AC (page 12 in book)
9 terms
Math Postulates
Midpoint Theorem:
Angle Bisector Theorem
Vertical Angles are congruent.
Theorem 2-4
If M is the midpoint of AB then AM = 1/2 AB and MB = 1/2 AB.
If BX is the bisector of <ABC then 1/2m<ABC and m <XBC and 1/…
<1 and <2 are vertical angles. <1 congruent to <2
If 2 lines are perpendicular, then they form congruent adjace…
Midpoint Theorem:
If M is the midpoint of AB then AM = 1/2 AB and MB = 1/2 AB.
Angle Bisector Theorem
If BX is the bisector of <ABC then 1/2m<ABC and m <XBC and 1/…
20 terms
Math Definitions Honors Geometry: Postulates and Theorem's
Theorem
Theorem 1
Deductive Structure
Postulate
A mathematical statement that can be proved
If two angles are right angles, then they are congruent
A system of thought in which conclusions are justified by mea…
a unproved assumption
Theorem
A mathematical statement that can be proved
Theorem 1
If two angles are right angles, then they are congruent
Geometry Postulates
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points there is exactly one line.
If two lines intersect, then they intersect in exactly one po…
If two planes intersect, then they intersect in exactly one l…
Through any three noncollinear points there is exactly one pl…
Postulate 1-1
Through any two points there is exactly one line.
Postulate 1-2
If two lines intersect, then they intersect in exactly one po…
8 terms
Geometry Postulates
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Through any two points there is exactly one line
If two lines intersect they intersect in exactly one point
If two planes intersect, they intersect in exactly one line
Through any three non-collinear points there exists exactly o…
Postulate 1
Through any two points there is exactly one line
Postulate 2
If two lines intersect they intersect in exactly one point
11 terms
Geometry 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 of ray OB. The r…
If P is in the interior of angle 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,…
9 terms
geometry postulates
Postulate 1- Ruler Postulate
Postulate 2- Segment Addition Postulate
Postulate 3
Postulate 4- Angle Addition Postulate
the points on a line can be paired with the real numbers in s…
ex. if B is between A and C then: AB+BC=AC
rays can be paired with the real numbers from 1-180
if a point lies in the interior of and angle, then you would…
Postulate 1- Ruler Postulate
the points on a line can be paired with the real numbers in s…
Postulate 2- Segment Addition Postulate
ex. if B is between A and C then: AB+BC=AC
15 terms
Geometry Pre AP postulates
ruler postulate
Segment Addition Postulate (Seg. Add.…
Protractor Postulate
Angle Addition Postulate
1.)points must be put on a number line... 2.)the distance betwee…
if B is between A and C, then AB+BC=AC (page 12 in book)
used to find the measure of an angle... 1.) take the absolute va…
m<AOB + m<BOC = m< AOC
ruler postulate
1.)points must be put on a number line... 2.)the distance betwee…
Segment Addition Postulate (Seg. Add.…
if B is between A and C, then AB+BC=AC (page 12 in book)
Geometry-Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on a line can be match one to one with real number…
If B is between A and C, then AB+BC=AC. If AB+BC=AC, then B i…
Consider a point A on one side of line OB. The rays of a form…
If P is in the interior of ∠RST, then m∠RSP+m∠PST=m∠RST.
Ruler Postulate
The points on a line can be match one to one with real number…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC. If AB+BC=AC, then B i…
21 terms
Postulates(Geometry)
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Postulate 1
Ruler Postulate
Postulate 2
Segment Addition Postulate
11 terms
Geometry Postulates
ruler postulate
segment addition postulate
protractor postulate
angle addition postulate
the points on a line can paired in a one-to-one correspondenc…
if B is between A and C, then AB + BC = AC
given a point X on line PR, consider rays XP and XR as well a…
if point D is in the interior of angle ABC, then m angleABD +…
ruler postulate
the points on a line can paired in a one-to-one correspondenc…
segment addition postulate
if B is between A and C, then AB + BC = AC
18 terms
Geometry Postulates
Postulate 1 - Ruler Postulate
Postulate 2 - Segment Addition Postulate
Postulate 3 - Protractor Postulate
Postulate 4 - 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 ... AND ... If AB + BC =…
<AOB is equal to the absolute value of the difference between…
If B is the interior of angle AOC, then the measure of angle…
Postulate 1 - Ruler Postulate
The points on a line can be matched one to one with the real…
Postulate 2 - Segment Addition Postulate
If B is between A and C, then AB + BC = AC ... AND ... If AB + BC =…
17 terms
Geometry Postulates
The Distance Postulate (2-4)
The Ruler Postulate (2-5)
The Ruler Placement Postulate (2-5)
The Line Postulate
To every pair of different points there corresponds a unique…
1. One point of the line for each number... 2. One number for ea…
Given 2 Points of a line, the coordinate system can be shifte…
For every two different points there is exactly one line that…
The Distance Postulate (2-4)
To every pair of different points there corresponds a unique…
The Ruler Postulate (2-5)
1. One point of the line for each number... 2. One number for ea…
12 terms
Big Ideas Math Geometry Chapter 6 Postulates, Properties, & Theorems
Perpendicular Bisector Theorem
Converse of the Perpendicular Bisector…
Angle Bisector Theorem
Converse of the Angle Bisector Theorem
In a plane, if a point lies on the perpendicular bisector of…
In a plane, if a point is equidistant from the endpoints of a…
If a point lies on the bisector of an angle, then it is ... equi…
If a point is in the interior of an angle and is equidistant…
Perpendicular Bisector Theorem
In a plane, if a point lies on the perpendicular bisector of…
Converse of the Perpendicular Bisector…
In a plane, if a point is equidistant from the endpoints of 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
10 terms
Geometry Postulates Chapter 1
Postulate 1-1 Through any two points,…
Postulate 1-2 If two distinct lines in…
Postulate 1-3 If two distinct _______i…
Postulate 1-4 Through any ________poin…
line
point
planes
three noncollinear
Postulate 1-1 Through any two points,…
line
Postulate 1-2 If two distinct lines in…
point
28 terms
Geometry Postulates/Axioms
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulates
Distance between two points A and B on a line can be found by…
If B is between AC, then AB + BC = AC
Think about protractor :)
If C is the interior angle of AOD, then ∠AOD = ∠AOC + ∠COD
Ruler Postulate
Distance between two points A and B on a line can be found by…
Segment Addition Postulate
If B is between AC, then AB + BC = AC
19 terms
Geometry Postulates
Ruler Postulate
Segment Addition Postulate
Angle Addition Postulate
Linear Pair Postulate
The distance between points A and B, written as AB, is the ab…
If B is between A and C, then AB + BC=AC. If AB+BC=AC, then B…
If P is in the interior of (a)RST, then m(a) RSP+m(a)PST=m(a)…
If two angles form a linear pair,then they are supplementary.
Ruler Postulate
The distance between points A and B, written as AB, is the ab…
Segment Addition Postulate
If B is between A and C, then AB + BC=AC. If AB+BC=AC, then B…
13 terms
geometry postulates and theroms
points existence postulate
straight line postulate
plane postulate
flat plane postulate
space contains at least four noncoplanar points. every plane…
two points are contained in one and only one line (two points…
three noncollinear points are contained in one and only one p…
if two points are in a plane, then the line containing the po…
points existence postulate
space contains at least four noncoplanar points. every plane…
straight line postulate
two points are contained in one and only one line (two points…
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