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Study sets matching "postulates geometry math theorems corollaries"

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Study sets matching "postulates geometry math theorems corollaries"

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…
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
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
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…
128 terms
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…
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…
69 terms
Geometry Postulates, Theorems, and Corollaries
Segment Addition Postulate
Angle Addition Postulate
Points of Figures Postulate
Points and Lines Postulate
AB + BC= AC
m∠ABZ+m∠ZBC=m∠ABC
A line contains at least wo points, a plane contains atleast…
Through any two points there is one line
Segment Addition Postulate
AB + BC= AC
Angle Addition Postulate
m∠ABZ+m∠ZBC=m∠ABC
12 terms
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
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
41 terms
Geometry Postulates/ Theorems/ Corollaries
diagonals of a rectangle
triangle inequality theorem
midpoint theorem
addition property of equality
if the diagonals of a parallelogram are congruent, then the p…
the sum of the lengths of any two sides of a triangle must be…
if M is the midpoint of AB than AM = BM
a=b then a+c= b+c
diagonals of a rectangle
if the diagonals of a parallelogram are congruent, then the p…
triangle inequality theorem
the sum of the lengths of any two sides of a triangle must be…
17 terms
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 2 points lie in a plane, then the line containing those po…
if 2 lines intersect they intersect at exactly 1 point
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…
23 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 three sides of one triangle are congruent to three sides o…
If two sides and the included angle of one triangle are congr…
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
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…
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,…
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
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
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…
54 terms
Geometry Postulates, Theorems, and Corollaries
Third Angles Theorem
SSS Postulate
SAS postulate
ASA postulate
If two angles of one triangle are congruent to two angles of…
If the three sides of one triangle are congruent to the three…
If two sides and the included angle of one triangle are congr…
If two angles and the included side of one triangle are congr…
Third Angles Theorem
If two angles of one triangle are congruent to two angles of…
SSS Postulate
If the three sides of one triangle are congruent to the three…
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…
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…
68 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
128 terms
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
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.
121 terms
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…
15 terms
Math Theorems, Corollaries, and Postulates
Side Angle Side Theorem
Base Angles Theorem
CITT (Converse to ITT)
ITT (Isosceles Triangle 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 two sides of a triangle are congruent , then the angles op…
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…
44 terms
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…
25 terms
Geometry: Postulates, Theorems, and Corollaries Definitions
Postulate
Theorem
Corollary
Segment Addition Postulate
A statement that is accepted as true without proof
Any statement that can be proven
A theorem whose proof comes directly from another theorem.
If B is between A and C, then AB+BC=AC.
Postulate
A statement that is accepted as true without proof
Theorem
Any statement that can be proven
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…
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
44 terms
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…
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…
33 terms
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
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…
56 terms
Geometry Vocabulary, Theorems, Postulates, and Corollaries
Point
Line
Line Segment
Plane
Does not have any size or shape; Used to identify a location
Extends forever in two directtions; There is no infinite numb…
A line connected by two endpoints
Extends forever with no thickness; Must have at least 3 points
Point
Does not have any size or shape; Used to identify a location
Line
Extends forever in two directtions; There is no infinite numb…
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…
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
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…
...
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
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
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…
102 terms
Geometry postulates, theorems, corollary, properties
Properties of kites
Isoceles trapezoids theorem
Conditional statement
Hypothesis
Perpendicular diagonals, one pair of congruent opposite angles
Each pair of base angles are congruent, if and only if diagon…
If p, then q
If p part of conditional statement
Properties of kites
Perpendicular diagonals, one pair of congruent opposite angles
Isoceles trapezoids theorem
Each pair of base angles are congruent, if and only if diagon…
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…
19 terms
Math midterm postulates and theorems and corollaries
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Through any two points there is exactly one line
If two distinct lines intersect, they intersect at one point
If two distinct planes intersect, they intersect at a line
Through any three non collinear points there is exactly one p…
Postulate 1
Through any two points there is exactly one line
Postulate 2
If two distinct lines intersect, they intersect at one point
72 terms
Geometry Advanced Postulates, Rules, Corollaries, and Theorems
Ruler Postulate
Segmant 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, the AB + BC = AC
one ray of an angle can be paired with 0 degrees and its oppo…
if you have two angles that share a common ray, you can add t…
Ruler Postulate
the points on a line can be matched one to one with the real…
Segmant Addition Postulate
if B is between A and C, the AB + BC = AC
9 terms
Assignment 6 Postulates/Theorems/Corollaries Geometry
AA Similarity Postulate
SAS Similarity Theorem
SSS Similarity Theorem
Triangle Proportionality Theorem/Side…
If two angles of one triangle are congruent to two angles of…
If an angle of one triangle is congruent to an angle of anoth…
If the sides of two angles are in proportion, then the triang…
If a line parallel to one side of a triangle intersects the o…
AA Similarity Postulate
If two angles of one triangle are congruent to two angles of…
SAS Similarity Theorem
If an angle of one triangle is congruent to an angle of anoth…
35 terms
Chapter 1-3 Geometry Postulates, Theorems, and Corollaries
true
false
true
false
Through any 2 points there is exactly one line (t or f)
Through any 2 points there isn't always a line (t or f)
Through any 3 noncollinear points there is exactly one plane…
Through any 4 noncollinear points there is exactly one plane…
true
Through any 2 points there is exactly one line (t or f)
false
Through any 2 points there isn't always a line (t or f)
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