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Study sets matching "geometry theorems postulates"

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Study sets matching "geometry theorems postulates"

39 terms
Geometry Definitions, Theorems, and Postulates
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 exact…
if two distinct planes intersect, then they intersect in exac…
through any three non-collinear points there is exactly one p…
postulate 1-1
through any two points there is exactly one line
postulate 1-2
if two distinct lines intersect, then they intersect in exact…
41 terms
Geometry Theorems and Postulates
The ruler postulate
Segment addition postulate
Protractor postulate
Angle addition postulate
The points on a line can be put into one-to-one correspondenc…
If B is between A and C, then AB+BC=AC
Given line AB and point O on line AB, all rays that can be dr…
If S is in the interior of angle PQR, then measure of angle P…
The ruler postulate
The points on a line can be put into one-to-one correspondenc…
Segment addition postulate
If B is between A and C, then AB+BC=AC
30 terms
Geometry theorems and postulates
HL congruence theorem
SSS
ASA
SAS
If the hypotenuse and a leg of a right triangle are congruent…
If all the sides are congruent
Two angles and the included side is congruent
Two sides and the included angle are congruent
HL congruence theorem
If the hypotenuse and a leg of a right triangle are congruent…
SSS
If all the sides are congruent
27 terms
Geometry Postulates and Theorems
expansion
line
flat plane
plane intersection
Which postulate states that a line contains at least two poin…
Which postulate states that any two points in space lie in ex…
Which postulate states if two points lie in a plane, then the…
Which postulate states if two planes intersect, then their in…
expansion
Which postulate states that a line contains at least two poin…
line
Which postulate states that any two points in space lie in ex…
90 terms
Geometry theorems,postulates,definitions
space
collinear points
coplanar points
intersection
the set of all points
points all in one line
points all in one plane
the set of points that are in both figures
space
the set of all points
collinear points
points all in one line
32 terms
Geometry Postulates, Definitions, and Theorems
reflexive property
symmetric property
transitive of equality (inequality)
communative with respect to addition
If x=x, then x=x.
If x=y, then y=x.
If x=y and y=z, then x=z. (same for inequality)
If a+b+c, then a+c+b.
reflexive property
If x=x, then x=x.
symmetric property
If x=y, then y=x.
33 terms
Geometry Definitions, Theorems, and Postulates
Def. of Congruent
Def. of Midpoint
Def. of Segment bisector
Def. of Acute angle
If 2 segments, or angles equal each other they are congruent.
A point on a line segment that divides it into two equal parts.
A line, ray or segment which cuts another line segment into t…
An angle that is less than 90 degrees.
Def. of Congruent
If 2 segments, or angles equal each other they are congruent.
Def. of Midpoint
A point on a line segment that divides it into two equal parts.
43 terms
Geometry Theorems and Postulates
Congruent Supplements Theorem
Congruent Complements Theorem
Linear Pair Postulate
Vertical Angle Theorem
If two angles are supplementary to the same or congruent angl…
If two angles are complementary to the same or congruent angl…
If two angles form a linear pair, then they are supplementary
Vertical angles are congruent
Congruent Supplements Theorem
If two angles are supplementary to the same or congruent angl…
Congruent Complements Theorem
If two angles are complementary to the same or congruent angl…
12 terms
Geometry Postulates and Theorems
Postulate One (Ruler Postulate)
Postulate Two (Segment Addition Postul…
Postulate Three (Protractor Postulate)
Postulate Four (Angle Addition Postula…
The points on a line can be paired with the real numbers so t…
If B is between A and C, then AB + BC =AC
On line AB, choose any point O between A and B. Ray OA is pai…
If point B lies in the interior of <AOC, then ... m<AOB + m<BOC…
Postulate One (Ruler Postulate)
The points on a line can be paired with the real numbers so t…
Postulate Two (Segment Addition Postul…
If B is between A and C, then AB + BC =AC
31 terms
Geometry Postulates/Theorems/Vocab
inductive reasoning
conjecture
counterexample
conditional
the observance of a pattern in order to form a conclusion
the conclusion you reach through inductive reasoning
an example that proves something false
sentence written in if-then format
inductive reasoning
the observance of a pattern in order to form a conclusion
conjecture
the conclusion you reach through inductive reasoning
27 terms
Geometry Postulates, Theorems, and Definitions
Adjacent Angles
Bisector of an angle
Bisector of a segment
Collinear points
Two angles in a plane that have a common vertex and a common…
The ray that divides the angle into two congruent adjacent an…
A line, segment, ray or plane that intersects the segment at…
Points all in one line.
Adjacent Angles
Two angles in a plane that have a common vertex and a common…
Bisector of an angle
The ray that divides the angle into two congruent adjacent an…
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…
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
48 terms
Geometry Theorems, Definitions, and Postulates
Midpoint Theorem
Linear Pair Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
If M is the midpoint of ĀB, then ĀM~MB
If two angles form a linear pair, then they are supplementary
If two angles are supplementary to the same angle (or two con…
If two angles are complementary to the same angle (or two con…
Midpoint Theorem
If M is the midpoint of ĀB, then ĀM~MB
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary
26 terms
Geometry Definitions, Postulates and Theorems
Complementary Angles
Supplementary Angles
Theorem
Vertical Angles
Two angles whose measures have a sum of 90
Two angles whose measures have a sum of 180
A statement that can be proven
Tow angles formed by intersecting lines and facing in the opp…
Complementary Angles
Two angles whose measures have a sum of 90
Supplementary Angles
Two angles whose measures have a sum of 180
31 terms
Geometry theorems and postulates
Segment addition postulate
Angle addition postulate
Two point postulate
Line point postulate
If B is between A and C, then AB+CD=AC. If AB+BC=AC, then B i…
If P is in the interior of angle RST, then the measure of ang…
Through any two points, there exists exactly one line.
A line contains at least two points.
Segment addition postulate
If B is between A and C, then AB+CD=AC. If AB+BC=AC, then B i…
Angle addition postulate
If P is in the interior of angle RST, then the measure of ang…
11 terms
Geometry Theorems and Postulates
Reflexive Property
Side Side Side
Side Angle Side
Angle Side Angle
Any segment or angle is congruent to itself
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 include side of one triangle are congru…
Reflexive Property
Any segment or angle is congruent to itself
Side Side Side
If three sides of one triangle are congruent to three sides o…
21 terms
Geometry theorems and postulates
reflexive postulate
addition postulate
subtraction postulate
substitution postulate
A quantity is congruent to itself a=a.
If equal quantities are added to equals quantities, the sums…
If equal quantities are subtracted from equal quantities, the…
A quantity may be substituted for its equal in any expression.
reflexive postulate
A quantity is congruent to itself a=a.
addition postulate
If equal quantities are added to equals quantities, the sums…
175 terms
Geometry Terms, Theorems, and Postulates
Point
Line
Plane
Segment
Has no dimension. Represented by a dot
Has one dimension. Represented by a line with two arrowheads,…
Has two dimensions. Represented by a shape that looks like a…
Consists of two endpoints and all points between the two endp…
Point
Has no dimension. Represented by a dot
Line
Has one dimension. Represented by a line with two arrowheads,…
9 terms
Geometry Theorems & Postulates
Corresponding angles postulate
Alternate interior angles theorem
Same-side interior angles theorem
Alternate exterior angles theorem
If a transversal intersects two parallel lines, then correspo…
If a transversal intersects two parallel lines, then the alte…
If a transversal intersects two parallel lines, then same-sid…
If a transversal intersects two parallel lines, then alternat…
Corresponding angles postulate
If a transversal intersects two parallel lines, then correspo…
Alternate interior angles theorem
If a transversal intersects two parallel lines, then the alte…
16 terms
Geometry Theorems and Postulates
Congruent Complements Theorem
Right Angle Congruence Theorem
Vertical Angles Theorem
Corresponding Angles Postulate
If two angles are complementary to the same angle, then they…
All right angles are congruent
If two angles are vertical angles, then they are congruent
Corresponding angle pairs are congruent
Congruent Complements Theorem
If two angles are complementary to the same angle, then they…
Right Angle Congruence Theorem
All right angles are congruent
101 terms
Geometry - Vocab, Theorems, and Postulates
Acute Angle
Angle
Angle Bisector
Axiom
An angle is acute, if and only if, it has a measure greater t…
Two rays, or segments, with the same endpoint form an angle.
A ray that divides an angle into two congruent angles.
An accepted statement of fact; postulate.
Acute Angle
An angle is acute, if and only if, it has a measure greater t…
Angle
Two rays, or segments, with the same endpoint form an angle.
14 terms
Geometry Theorems & Postulates
Corresponding Angles Postulate
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
Same-side Interior Angles Theorem
corresponding angles are congruent
alternate interior angles are congruent
alternate exterior angles are congruent
same-side interior angles are supplementary
Corresponding Angles Postulate
corresponding angles are congruent
Alternate Interior Angles Theorem
alternate interior angles are congruent
16 terms
geometry theorems and postulates
if M is the midpoint of AB
through a line and a point not in the…
if two lines intersect
if BX is the bisector of angle ABC
AM = 1/2AB and MB = 1/2 AM
there is exactly one plane
exactly one plane contains the lines
measurement of angle ABX = 1/2 measurement of angle ABC
if M is the midpoint of AB
AM = 1/2AB and MB = 1/2 AM
through a line and a point not in the…
there is exactly one plane
12 terms
Geometry Theorems and Postulates
side XY is congruent to side XZ
Triangle Sum Thm.
Isosceles Triangle Thm.
two congruent sides
Since XY equals XZ
M<X + M<Y + M<Z = 180
base angles Z & Y are congruent so m<Z = M<Y
Isosceles Triangles have at least
side XY is congruent to side XZ
Since XY equals XZ
Triangle Sum Thm.
M<X + M<Y + M<Z = 180
35 terms
Geometry - Postulates, Theorems, & Properties
Postulate 5
Postulate 6
Postulate 8
Postulate 9
Through any 2 points there exists exactly one line
A line contains at least 2 points
Through any 3 non-collinear points there exists exactly one p…
A plane contains at least 3 noncollinear points
Postulate 5
Through any 2 points there exists exactly one line
Postulate 6
A line contains at least 2 points
42 terms
Geometry: Theorems, Postulates, and Terms
Vertical Angle Theorem
Adjacent Angle
Complementary Angle
Supplementary angle
Vertical Angles are congruent
A pair of angles in the same plane that meet the following co…
2 angles whose measures add up to 90 degrees
2 angles whose measures add up to 180 degrees
Vertical Angle Theorem
Vertical Angles are congruent
Adjacent Angle
A pair of angles in the same plane that meet the following co…
35 terms
Geometry Theorems and Postulates
If there are two points,
If there is a line,
Two points determine a ____
If there are three noncollinear points,
there is exactly one line that contains them.
then there are at least two points on the line
line
there is exactly one plane that contains them
If there are two points,
there is exactly one line that contains them.
If there is a line,
then there are at least two points on the line
44 terms
Geometry - Postulates, Theorems and Definitions
Commutative Property
Associative Property
Distributive Property
Transitive Property
a+b=b+a or ab=ba
(a+b)+c=a+(b+c)
a(b+c)=ab+ac
If a=b and b=c, then a=c
Commutative Property
a+b=b+a or ab=ba
Associative Property
(a+b)+c=a+(b+c)
91 terms
Geometry Theorems, Postulates, and Definitions
Segment Addition Postulate
Alternate Interior Angles Theorem
Same Side Interior Angles Theorem
Alternate Exterior Angles Thereom
If 3 points A, B, and C are collinear and B is between A and…
If two parallel lines are cut by a transversal line, then alt…
If 2 parallel lines in a plane are cut by a transversal line,…
If 2 parallel lines are cut by a transversal, then alternate…
Segment Addition Postulate
If 3 points A, B, and C are collinear and B is between A and…
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal line, then alt…
68 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
Geometry Postulates, Properties, & Theorems
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Perpendicular Lines
A=A
A=B... B=A
If A=B & B=C, then A=C
Lines that intersect and form right angles
Reflexive Property of Equality
A=A
Symmetric Property of Equality
A=B... B=A
24 terms
Geometry Definitions, Postulates, and Theorems
Addition Property
Subtraction Property
Multiplication Property
Division Property
Adding on both sides of the equal sign
Subtracting on both sides of the equal sign
Multiplying on both sides of the equal sign
Dividing on both sides of the equal sign
Addition Property
Adding on both sides of the equal sign
Subtraction Property
Subtracting on both sides of the equal sign
10 terms
Geometry Theorems and Postulates
Linear Pair Theorem
Congruent Supplement Theorem
Right Angle Congruence Theorem
Congruent Complementary Theorem
If two angles form a linear pair, then they are supplementary.
If two angles are supplementary to the same angle (or to two…
All right angles are congruent
If two angles are complementary to the same angle (or two con…
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary.
Congruent Supplement Theorem
If two angles are supplementary to the same angle (or to two…
42 terms
Postulates/Theorems for Geometry
Addition Propery 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 a•c=b•c
If a=b, then a÷c=b÷c
Addition Propery of Equality
If a=b, then a+c=b+c
Subtraction Property of Equality
If a=b, then a-c=b-c
80 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 exact…
If two distinct planes intersect, then they intersect in exac…
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 distinct lines intersect, then they intersect in exact…
30 terms
Geometry Postulates/Theorems
addition postulate
subtraction postulate
multiplication postulate
division postulate
if =/≅'s are added to =/≅, then the sums are =/≅
if =/≅'s are subtracted from =/≅'s, then the differences are…
if =/≅'s are multiplied by =/≅'s , then the products are =/≅
if =/≅'s are divided by =/≅'s then the quotients are =/≅
addition postulate
if =/≅'s are added to =/≅, then the sums are =/≅
subtraction postulate
if =/≅'s are subtracted from =/≅'s, then the differences are…
33 terms
Geometry Definitions, Postulates , and Theorems
Angle Addition Postulate
Right Angle Congruence
Linear Pair Theorem
Vertical Angle Theorem
The measure of two smaller angles equals the measure of a lar…
All right angles are congruent.
If two angles are a linear pair (adjacent and make a line), t…
If two angles are vertical angles, then they are congruent.
Angle Addition Postulate
The measure of two smaller angles equals the measure of a lar…
Right Angle Congruence
All right angles are congruent.
21 terms
Geometry Test Theorems and Postulates
right angles congruence theorem
congruent supplements theorem
congruent complements theorem
linear pair postulate
all right angles are congruent
if two angles are supplementary to the same angle (or to cong…
if two angles are complementary to the same angle (or to cong…
if two angles form a linear pair, then they are supplementary.
right angles congruence theorem
all right angles are congruent
congruent supplements theorem
if two angles are supplementary to the same angle (or to cong…
70 terms
Geometry: Terms, Postulates, and Theorems
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…
126 terms
Theorems and Postulates in Geometry
What is a net?
What is an isometric drawing?
What is an orthographic drawing?
What is a Point?
A net is a two-dimensional diagram that you can fold to form…
A drawing that shows a corner view of a 3D figure.
A drawing that shows the front, right, and top view of a 3D f…
indicates a location(is of no size value). Classified as the…
What is a net?
A net is a two-dimensional diagram that you can fold to form…
What is an isometric drawing?
A drawing that shows a corner view of a 3D figure.
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
73 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
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…
44 terms
Geometry postulates theorems and constructions
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 exact…
If two distinct planes intersect, then they intersect in exac…
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 distinct lines intersect, then they intersect in exact…
79 terms
Geometry Theorems, Postulates, and Definitions
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 paired with real numbers in such…
If B is between A and C, then AB+ BC= AC
If in <QOA, Ray OP lies inside of the angle, ... <QOP=<QOA-<POA
If point B lies on the interior of angle AOC, then angle AOB+…
Postulate 1 (Ruler Postulate)
The points on a line can be paired with real numbers in such…
Postulate 2 (Segment Addition Postulate)
If B is between A and C, then AB+ BC= AC
48 terms
Geometry Theorems/Postulates-Final
midsegment theorem
perpendicular bisector theorem
converse of the perpendicular bisector…
concurrency of perpendicular bisectors…
the segment connecting the midpoints of two sides of a triang…
in a plane, if a point is on the perpendicular bisector of a…
in a plane, if a point is equidistant from the endpoints of a…
the perpendicular bisectors of a triangle intersect at a poin…
midsegment theorem
the segment connecting the midpoints of two sides of a triang…
perpendicular bisector theorem
in a plane, if a point is on the perpendicular bisector of a…
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…
36 terms
Geometry: Definitions, Postulates, and Theorems
Reflexive Property Congruence
Symmetric Property Congruence
Transitive Property Congruence
Right Angles Congruence Theorem
If AB = AB, then AB = AB.
If AB = CD, then CD = AB.
If AB = CD and CD = EF, then AB = EF.
All right angles are congruent.
Reflexive Property Congruence
If AB = AB, then AB = AB.
Symmetric Property Congruence
If AB = CD, then CD = AB.
67 terms
Geometry Theorems and Postulates
Triangle Sum Theorem
Exterior Angle Theorem
Corollary
Definition of Congruent Polygons
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…
A statement that follows directly from a theorem.
Two shapes/figures are congruent if and only if all of their…
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…
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