Study sets matching "postulates geometry math theorems corollaries"

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Study sets matching "postulates geometry math theorems corollaries"

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…
35 terms
Geometry Postulates, Theorems, and Corollaries
Theorem 5.3 (Circumcenter Theorem)
Theorem 5.4 (Angle Bisector Theorem)
Theorem 5.5 (Converse of the Angle Bis…
Theorem 5.6 (Incenter Theorem)
The perpendicular bisectors of a triangle intersect at a poin…
If a point is on the bisectors of an angle, then it is equidi…
If a point in the interior of an angle is equidistant from th…
The angle bisectors of a triangle intersect at a point called…
Theorem 5.3 (Circumcenter Theorem)
The perpendicular bisectors of a triangle intersect at a poin…
Theorem 5.4 (Angle Bisector Theorem)
If a point is on the bisectors of an angle, then it is equidi…
Geometry Theorems/Postulates/Corollaries
Linear Pair Postulate
Corresponding Angles Postulate
Two Perps Theorem
Perpendicular Transversal Theorem
If two angles form a linear pair, then they are supplementary.
If two parallel lines are cut by a transversal, then the pair…
If two lines are perpendicular to the same line, then the lin…
If a line is perpendicular to one of two parallel lines, then…
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pair…
Geometry Postulates, Theorems, and Corollaries
Right Angles Congruence Theorem
Midpoint Theorem
Ruler Postulate
Segment Addition Postulate
All right angles are congruent
If M is the midpoint of line segment AB, then line segment AM…
Given any 2 points A and B on a line, if A corresponds to 0,…
If A, B, and C are collinear and AB+BC=AC, then B is between…
Right Angles Congruence Theorem
All right angles are congruent
Midpoint Theorem
If M is the midpoint of line segment AB, then line segment AM…
45 terms
Geometry - Postulates, Theorems, & Corollaries
Segment Addition Postulate
Angle Addition Postulate
Pythagorean Theorem
Linear Pair Theorem
If B is between A and C, then AB + BC = AC
If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR
In a right triangle, the sum of the squares if the lengths of…
If two angles form a linear pair then they are supplementary
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate
If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR
18 terms
Geometry Theorems/Postulates/Corollaries
Theorem 4.1
Theorem 4.2
Theorem 4.3
Corollary 4.1
Angle Sum Theorem- The sum of the measures of the angles of a…
Third Angle Theorem- If two angles of one triangle are congru…
Exterior Angle Theorem- The measure of an exterior angle of a…
The acute angles of a right triangle are complementary.
Theorem 4.1
Angle Sum Theorem- The sum of the measures of the angles of a…
Theorem 4.2
Third Angle Theorem- If two angles of one triangle are congru…
50 terms
geometry postulates and theorems and corollaries
ruler postulate
segment addition postulate
protractor postulate
angle addition postulate
the points on a line can be paired with the real numbers in s…
if B is between A and C, than AB+BC= AC
ruler postulate w angles
if point B lies in the interior of ∠AOC than m∠AOB + m∠BOC =…
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, than AB+BC= AC
Formal Geometry; Postulates,Theorems, and Corollaries
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
If three sides of one triangle are congruent to the second tr…
If two sides and the included angle of one triangle are congr…
If two sides and the included side of one triangle are congru…
If two angles and a non included side of one triangle are con…
Side-Side-Side (SSS)
If three sides of one triangle are congruent to the second tr…
Side-Angle-Side (SAS)
If two sides and the included angle of one triangle are congr…
Geometry Postulates, Theorems, Corollaries
Post 1-1-1
Post 1-1-2
Post 1-1-3
Post 1-1-4
Through any two points there is exactly one line
Through any three non-collinear points there is exactly one p…
If two points lie in a plane, then the line containing those…
If two lines intersect, then they intersect in exactly one po…
Post 1-1-1
Through any two points there is exactly one line
Post 1-1-2
Through any three non-collinear points there is exactly one p…
Geometry (Postulates, Theorems, Corollaries)
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…
Geometry Theorems, Postulates, and Corollaries
If two angles of one triangle are cong…
Each angle of an equiangular triangle…
In a triangle there can be at most
Supplementary Angle Theorem
then the third angles are congruent too
sixty degrees
one right angle or one obtuse angle
All angles which are supplementy to the same or equal angles…
If two angles of one triangle are cong…
then the third angles are congruent too
Each angle of an equiangular triangle…
sixty degrees
38 terms
Geometry Postulated, Theorems and Corollaries
Postulate 2.1
Postulate 2.2
Postulate 2.3
Postulate 2.4
Through any two points, there is exactly one line.
Through any three points not on the same line, there is exact…
...
...
Postulate 2.1
Through any two points, there is exactly one line.
Postulate 2.2
Through any three points not on the same line, there is exact…
163 terms
Geometry Theorems, Postulates, and Corollaries
postulate 1 - ruler postulate
postulate 2 - segment addition postulate
postulate 3 - protractor postulate
postulate 4 - 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 ab in a given plane, choose any point o between a and b. c…
if point b lies in the interior of <aoc, then m<aob + m<boc =…
postulate 1 - ruler postulate
1. the points on a line can be paired with the real numbers i…
postulate 2 - segment addition postulate
if b is between a and c, then ab + bc = ac
111 terms
Geometry Postulates, Theorems, and Corollaries
Postulate 1
Postulate 2:
Postulate 3:
Postulate 4:
Ruler Postulate: The points on a line can be paired in a one…
Segment Addition Postulate:... If B is between A and C, then AB…
Protractor Postulate:... Given a point, X, on line PR, consider…
Angle Addition Postulate:... If point D is in the interior of <A…
Postulate 1
Ruler Postulate: The points on a line can be paired in a one…
Postulate 2:
Segment Addition Postulate:... If B is between A and C, then AB…
Geometry Postulates, Theorems, and Corollaries
Postulate 1
Postulate 2:
Postulate 3:
Postulate 4:
Ruler Postulate: The points on a line can be paired in a one…
Segment Addition Postulate:... If B is between A and C, then AB…
Protractor Postulate:... Given a point, X, on line PR, consider…
Angle Addition Postulate:... If point D is in the interior of <A…
Postulate 1
Ruler Postulate: The points on a line can be paired in a one…
Postulate 2:
Segment Addition Postulate:... If B is between A and C, then AB…
23 terms
Geometry Postulates, Corollaries, and Theorems
Perpendicular Transversal Theorem
Lines Perpendicular to a Transversal T…
6 Vertical Angles Congruence Theorem
Parallel Postulate
If a transversal is perpendicular to one of two parallel line…
In a plane, if two lines are perpendicular to the same line,…
Vertical Angles are congruent.
If there is a line and a point not on the line, then there is…
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel line…
Lines Perpendicular to a Transversal T…
In a plane, if two lines are perpendicular to the same line,…
162 terms
Geometry Postulates, Theorems, and Corollaries
2.1: Points, Lines, and Planes Postulate
2.2: Points, Lines, and Planes Postulate
2.3: Points, Lines, and Planes Postulate
2.4: Points, Lines, and Planes Postulate
Through any two points, there is exactly one line
Through any three non-collinear points, there is exactly one…
A line contains at least two points
A plane contains at three non-collinear points
2.1: Points, Lines, and Planes Postulate
Through any two points, there is exactly one line
2.2: Points, Lines, and Planes Postulate
Through any three non-collinear points, there is exactly one…
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
Math - Postulates, Theorems, and Corollaries
A point on the perpendicular bisector…
A point equidistant from the endpoints…
A point on the bisector of an angle is
A point on or in the interior of an an…
equidistant from the endpoints of the segments
perpendicular bisector of the segement
equidistant from the sides of the angle
sides of an angle lies on the bisector of the angle
A point on the perpendicular bisector…
equidistant from the endpoints of the segments
A point equidistant from the endpoints…
perpendicular bisector of the segement
76 terms
Geometry Postulates, Theorems, and Corollaries
Postulate 1 (Ruler Postulate)
Postulate 2 (Segment Addition Postulate)
Postulate 3 (Protractor Postulate)
Postulate 4 (Angle Addition Postulate)
1. The points on a line can be paired with the real numbers 0…
If B is between A and C, then AB + BC = AC
On line AB in a given line, choose any point O between A and…
If point B lies in the interior of the angle AOC, then the me…
Postulate 1 (Ruler Postulate)
1. The points on a line can be paired with the real numbers 0…
Postulate 2 (Segment Addition Postulate)
If B is between A and C, then AB + BC = AC
Geometry Postulates, Theorems, and Corollaries
Right Angles Congruence Theorem
Midpoint Theorem
Ruler Postulate
Segment Addition Postulate
All right angles are congruent
If M is the midpoint of line segment AB, then line segment AM…
Given any 2 points A and B on a line, if A corresponds to 0,…
If A, B, and C are collinear and AB+BC=AC, then B is between…
Right Angles Congruence Theorem
All right angles are congruent
Midpoint Theorem
If M is the midpoint of line segment AB, then line segment AM…
140 terms
Geometry Theorems, Corollaries, and Postulates
Ruler postulate
Segment addition postulate
Protractor postulate
Angle addition postulate
1. The points on a line can be paired with real numbers in su…
If B is between A and C the AB + BC = AC
Use a protractor to measure angles
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 real numbers in su…
Segment addition postulate
If B is between A and C the AB + BC = AC
Geometry- Theorems, Postulates, and Corollaries
(Postulate 1-5) Ruler Postulate
(Postulate 1-7) Protractor Postulate
(Postulate 1-8) Angle Addition Postulate
(Postulate 1-9) Linear Pair Postulate
Every point on a line can be paired with a real number. This…
Consider ray OB and a point A on one side of ray OB. Every fo…
If point B is in the interior of angle <AOC, then m<AOB + m<B…
If 2 angles form a linear pair, then they are supplementary
(Postulate 1-5) Ruler Postulate
Every point on a line can be paired with a real number. This…
(Postulate 1-7) Protractor Postulate
Consider ray OB and a point A on one side of ray OB. Every fo…
Math Theorems, Corollaries, and Postulates
Side Angle Side Theorem
Base Angles Theorem
CITT (Converse to ITT)
Corollary to the Base Angles Theorem
If 2 pairs of corresponding sides and the included angles in…
If two sides of a triangle are congruent the the angles oppos…
If 2 angles of a triangle are congruent then the sides opposi…
If a triangle is equilateral then it's equalangular
Side Angle Side Theorem
If 2 pairs of corresponding sides and the included angles in…
Base Angles Theorem
If two sides of a triangle are congruent the the angles oppos…
Math Theorems, Corollaries, and Postulates
Betweenness of Points
Post 1
Post 2
Ruler Post
if A-B-C, then AB + BC... = AC
2 points determine a line
3 noncollinear points determine a plane
the points on a line can be numbered so that positive number…
Betweenness of Points
if A-B-C, then AB + BC... = AC
Post 1
2 points determine a line
27 terms
Geometry postulates, theorems, and corollaries
Postulate 10
Postulate 11
Postulate 12
Postulate 13
If two parallel lines are cut by a transversal, then correspo…
If two lines are cut by a transversal and corresponding angle…
If the three sides of a triangle are congruent to the corresp…
If two sides and the included angle of a triangle are congrue…
Postulate 10
If two parallel lines are cut by a transversal, then correspo…
Postulate 11
If two lines are cut by a transversal and corresponding angle…
24 terms
Geometry Postulates, Theorems, and Corollaries
Through any two points there is
Through any three noncollinear points…
If two points lie on a plane, then the…
Ruler Postulate
exactly one line
one plane containing them
lies in the plane
The points on a line can be put into a one-to-one corresponde…
Through any two points there is
exactly one line
Through any three noncollinear points…
one plane containing them
54 terms
Geometry Theorems, Postulates, and Corollary
Postulate 1 (Ruler)
Postulate 2 (Segment Addition)
Postulate 3 (Protractor)
Postulate 4 (Angle Addition)
1. The points on a line can be paired with the real numbers i…
If B is between A and C, then segment AB + segment BC = segme…
On line AB in a given place, choose any O between A and B. Co…
If point B lies in the interior of angle AOC then the measure…
Postulate 1 (Ruler)
1. The points on a line can be paired with the real numbers i…
Postulate 2 (Segment Addition)
If B is between A and C, then segment AB + segment BC = segme…
111 terms
Geometry: Postulates, Theorems and Corollaries
1-1-1 Postulate
1-1-2 Postulate
1-1-3 Postulate
1-1-4 Postulate
Through any two points there is exactly one line.
Through any three nonlinear points there is exactly one plane.
If two points lie in a plane then that line also lies on the…
If two lines intersect then they intersect in exactly one poi…
1-1-1 Postulate
Through any two points there is exactly one line.
1-1-2 Postulate
Through any three nonlinear points there is exactly one plane.
7 terms
Geometry Theorems, Postulates, and Corollary
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Two points determine a line
Three non collinear points determine a plane
The points on a line can be numbered so that positive number…
The rays in a half-rotation can be numbered from 0 to 180 so…
Postulate 1
Two points determine a line
Postulate 2
Three non collinear points determine a plane
118 terms
Math Midterm Theorems, Postulates, and Corollaries
Postulate 2 Segment Addition Postulate
Postulate 3
Postulate 4 Protractor Postulate
Postulate 5 Angle Addition Postulate
If C is between A and B, then AC + CB = AB.
Any segment has exactly one midpoint
In a given plane, select any line AB and any point C between…
If D is in the interior of angle ABC, then m angle ABC = m an…
Postulate 2 Segment Addition Postulate
If C is between A and B, then AC + CB = AB.
Postulate 3
Any segment has exactly one midpoint
17 terms
Geometry Theorems/ Postulates, Theorems, and Corollaries
Post. 1-1-1
Post. 1-1-2
Post. 1-1-3
Post. 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…
Post. 1-1-1
Through any two points there is exactly one line.
Post. 1-1-2
Through any three noncollinear points there is exactly one pl…
33 terms
Geometry Postulates, Theorems, and Corollaries
Through 2 points
Through any 3 points noncollinear
A line contains
If two points lie on a plane
There is only one line
There is only one plane
2 points
The entire line connecting them lies on that plane
Through 2 points
There is only one line
Through any 3 points noncollinear
There is only one plane
80 terms
Advanced Geometry Postulates, Theorems, and Corollaries
1-1-1 Points, Lines, and Planes
1-1-2 Points, Lines, and Planes
1-1-3 Points, Lines, and Planes
1-1-4 Intersection of Lines and Planes
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 plane containing those…
If two lines intersect, then they intersect in exactly one po…
1-1-1 Points, Lines, and Planes
Through any two points there is exactly one line.
1-1-2 Points, Lines, and Planes
Through any three noncollinear points there is exactly one pl…
107 terms
Math Midterm Theorems, Postulates, and Corollaries
Postulate 2 Segment Addition Postulate
Postulate 5 Angle Addition Postulate
Theorem 2.4 - Corollary
Postulate 8
If C is between A and B, then AC + CB = AB.
If D is in the interior of angle ABC, then m angle ABC = m an…
If two lines are perpendicular, then four right angles are fo…
A line contains at least two points. A plane contains at leas…
Postulate 2 Segment Addition Postulate
If C is between A and B, then AC + CB = AB.
Postulate 5 Angle Addition Postulate
If D is in the interior of angle ABC, then m angle ABC = m an…
Geometry final (postulates, theorems, corollaries)
Chapter 3:
Theorem 3-1
Postulate 10
Theorem 3-2
Chapter 3:
if 2 parallel planes are cut by a 3rd plane, then the lines o…
if 2 parallel lines are cut by a transversal, then correspond…
if 2 parallel lines are cut by a transversal, then alternate…
Chapter 3:
Chapter 3:
Theorem 3-1
if 2 parallel planes are cut by a 3rd plane, then the lines o…
142 terms
HN Geometry Theorems, Postulates, & Corollaries
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
1. The points on a line can be paired with real numbers in su…
If B is between A and C, then AB+BC= AC
On line 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 real numbers in su…
Segment Addition Postulate
If B is between A and C, then AB+BC= AC
72 terms
Geometry terms, postulates, theorems and corollaries
Acute triangle
Equiangular triangle
Obtuse triangle
Right triangle
A triangle in which all of the angles are acute. It has three…
A triangle with all angles congruent. It has three congruent…
A triangle with an obtuse angle. An obtuse angle is any angle…
A triangle with a right angle. A right angle is any angle tha…
Acute triangle
A triangle in which all of the angles are acute. It has three…
Equiangular triangle
A triangle with all angles congruent. It has three congruent…
33 terms
Geometry Vocabulary, Theorems, Corollaries, and Postulates
Point
Line
Plane
Colinear
A location. It has neither shape nor size.
Made up of two points and has no thickness or width. There ca…
Flat surface made up of points that extends infinitely in all…
Points that lie on the same line.
Point
A location. It has neither shape nor size.
Line
Made up of two points and has no thickness or width. There ca…
74 terms
GEOMETRY FINAL: POSTULATES, THEOREMS, AND COROLLARIES
(ch 1) through any two points there is…
(ch 1) through any three noncollinear…
(ch 1) if two points lie in a plane, t…
(ch 1) if two lines intersect, then th…
...
...
...
...
(ch 1) through any two points there is…
...
(ch 1) through any three noncollinear…
...
55 terms
Geometry Midterm Postulates, Theorems, and Corollaries
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
104 terms
Math Definitions, Postulates, Theorems, & Corollaries
Point
Line
Plane
Collinear Points
has no size; represented by a dot; named by a capital letter
series of points that extend in 2 opposite directions; named…
flat never ending surface; no thickness; named using multiple…
points that are on the same line
Point
has no size; represented by a dot; named by a capital letter
Line
series of points that extend in 2 opposite directions; named…
Formal Geometry; Postulates,Theorems, and Corollaries
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
If three sides of one triangle are congruent to the second tr…
If two sides and the included angle of one triangle are congr…
If two sides and the included side of one triangle are congru…
If two angles and a non included side of one triangle are con…
Side-Side-Side (SSS)
If three sides of one triangle are congruent to the second tr…
Side-Angle-Side (SAS)
If two sides and the included angle of one triangle are congr…
99 terms
HOLT: Geometry Postulates, Theorems, and Corollaries
Postulate 1-1-1
Postulate 1-1-2
Post 1-1-3
Post 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 at 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…
37 terms
honors geometry postulates, corollaries, and theorems
if A is between A and B, the, AB+BC=AC
if point B lies in the interior of <AO…
two
three
segment additions postulate
angle addition postulate
a line contains atleast __ points
a plane contains at lease ___ points not all in one line
if A is between A and B, the, AB+BC=AC
segment additions postulate
if point B lies in the interior of <AO…
angle addition postulate
51 terms
Geometry Axioms, Postulates, Corollaries, and Theorems
Reflexive Axiom
Symmetric Axiom
Addition Axiom
Multiplication Axiom
a=a
If a=b, then b=a
If a=b, then a+c=b+c *... *Also, if a=b and c=d, then a+c=b+d
If a=b, then ac=bc
Reflexive Axiom
a=a
Symmetric Axiom
If a=b, then b=a
59 terms
Honors Geometry Theorems and Postulates and Corollarys
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The distance between any 2 points on a number line is the abs…
If 3 points A, B, and C are collinear and B is between A and…
If P is in the interior of ∠RST, then ∠RSP+∠PST=∠RST
Ruler Postulate
The distance between any 2 points on a number line is the abs…
Segment Addition Postulate
If 3 points A, B, and C are collinear and B is between A and…
13 terms
Holt Geometry Chapter 4 Postulates, Theorems, and Corollaries
AAS Theorem: 4-5-2
The Isosceles Triangle Theorem: 4-8-1
Corollary of an equiangular triangle:…
Corollary of triangle: 4-2-3
If two angles and a non-included side of one triangle are con…
If two sides of a triangle are congruent, then the angles opp…
An equilateral triangle is also equiangular.
An equilateral triangle has three 60 Degree angles
AAS Theorem: 4-5-2
If two angles and a non-included side of one triangle are con…
The Isosceles Triangle Theorem: 4-8-1
If two sides of a triangle are congruent, then the angles opp…
95 terms
Geometry 1: Definitions, Postulates, Theorems, Corollaries
Two points determine a
Three noncollinear points determine a
The Pythagorean Theorem
The Triangle Sum Theorem
line
plane
The sum of the angles in a triangle is 180 degrees.
Two points determine a
line
Three noncollinear points determine a
plane
22 terms
Geometry Honors - Postulates & Theorems/Corollaries
The Ruler Postulate
The Protractor Postulate
Segment Addition Postulate/The Between…
Angle Addition Postulate/The Betweenne…
points on a line can be numbered so that positive number diff…
you can measure angles
If A-B-C, then AB + BC = AC
∠AOB + ∠BOC = ∠AOC
The Ruler Postulate
points on a line can be numbered so that positive number diff…
The Protractor Postulate
you can measure angles
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