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Study sets matching "geometry postulates math theorems"

17 terms
Math: Geometry theorems and postulates
Transitive Property
symmetric property
reflexive property
substitution property
if a=b and b=c then a=c
if a=b then b=a
for any real number a, a=a
if a=b then a can be substituted for binary equation/expression
Transitive Property
if a=b and b=c then a=c
symmetric property
if a=b then b=a
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…
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…
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…
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…
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…
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
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…
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,…
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…
64 terms
Geometry Postulates and Theorems
they are congruent.... Right Angles Cong…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Complem…
If two angles are right angles, then
If two angles are supplementary to the same angle, then
If two angles are supplementary to congruent angles, then
If two angles are complementary to the same angle, then
they are congruent.... Right Angles Cong…
If two angles are right angles, then
they are congruent.... Congruent Supplem…
If two angles are supplementary to the same angle, then
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…
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-…
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
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.
64 terms
Geometry Postulates and Theorems
they are congruent.... Right Angles Cong…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Complem…
If two angles are right angles, then
If two angles are supplementary to the same angle, then
If two angles are supplementary to congruent angles, then
If two angles are complementary to the same angle, then
they are congruent.... Right Angles Cong…
If two angles are right angles, then
they are congruent.... Congruent Supplem…
If two angles are supplementary to the same angle, then
14 terms
Geometry Theorems/Definitions/Postulates
Linear Pairs are Supplementary.
Perpendicular Lines form right angles.
All right angles are congruent.
Supplements of congruent angles are co…
Right
Supplementary (Working with total of 4 angles)
Linear Pairs are Supplementary.
Perpendicular Lines form right angles.
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
64 terms
Geometry Postulates and Theorems
they are congruent.... Right Angles Cong…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Complem…
If two angles are right angles, then
If two angles are supplementary to the same angle, then
If two angles are supplementary to congruent angles, then
If two angles are complementary to the same angle, then
they are congruent.... Right Angles Cong…
If two angles are right angles, then
they are congruent.... Congruent Supplem…
If two angles are supplementary to the same angle, then
19 terms
Geometry Honors Theorems & Postulates
Right Angle Congruence Theorem
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
If 2 angles are right angles, then they are congruent
If 2 angles are vertical angles, then they are congruent
If 2 angles are supplementary to the same angle or congruent…
If 2 angles are complementary to the same angle or congruent…
Right Angle Congruence Theorem
If 2 angles are right angles, then they are congruent
Vertical Angles Theorem
If 2 angles are vertical angles, then they are congruent
25 terms
Geometry Definitions/Theorems/Postulates
Midpoint
Collinear
Straight Angles
Acute Angles
It is a midpoint if and only if it divides a segment into two…
3 or more points on the same line
The sides of a straight angle form a line
Acute angles are less than a right angle
Midpoint
It is a midpoint if and only if it divides a segment into two…
Collinear
3 or more points on the same line
6 terms
Geometry Postulates & Theorems
Corresponding Angles Converse
Alternate Interior Angles Converse
Alternative Exterior Angles Converse
Consecutive Interior Angles converse
If two lines are cut by a transversal so the corresponding an…
If two lines are cut by a transversal so the alternate interi…
if two lines are cut by a transversal so the alternate exteri…
If two lines are cut by a transversal so the consecutive inte…
Corresponding Angles Converse
If two lines are cut by a transversal so the corresponding an…
Alternate Interior Angles Converse
If two lines are cut by a transversal so the alternate interi…
39 terms
Geometry Theorems, Postulates, & Definitions
Segment Addition Postulate
Angle Addition Postulate
Definition of Midpoint & Bisector
Definition of Angle Bisector
If B is between A and C then the length of AC is equal to the…
If P is in the interior of ∠RST then the measure of ∠RST is t…
A bisector bisects a line segment at its midpoint which divid…
A ray that divides an angle into two adjacent angles that are…
Segment Addition Postulate
If B is between A and C then the length of AC is equal to the…
Angle Addition Postulate
If P is in the interior of ∠RST then the measure of ∠RST is t…
81 terms
Geometry Theorems/Postulates/Definitions
theorem
postulate
definition
geometry
a statement that can be proved
something we don't need to prove, uses past information to ba…
assigns a term to an object. are always reversible
to take a series of facts to put in a logical way to reach a…
theorem
a statement that can be proved
postulate
something we don't need to prove, uses past information to ba…
16 terms
Important Geometry Theorems/Postulates
If two congruent angles form a linear…
If two angles are vertical angles, the…
If there is a line and a point not on…
If there exists a line and a point, th…
If two congruent angles form a linear…
If two angles are vertical angles, the…
12 terms
Geometry - Postulates and theorems
segment addition postulate
reflexive property
congruent
midpoint theorem
AB + BC = AC
any segment or angle is congruent/equal to itself (AB = AB) (…
have equal measure
If AB + BC = AC and AB=BC
segment addition postulate
AB + BC = AC
reflexive property
any segment or angle is congruent/equal to itself (AB = AB) (…
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,…
18 terms
Geometry Postulates and Theorems
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, then AB + BC = AC.
Given line AB and a point O on line AB, all rays that can be…
If B is in the interior of <AOC, then m<AOB + m<BOC = m<AOC.
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, then AB + BC = AC.
16 terms
Geometry Postulates and Theorems
corresponding angles
congruent corresponding angles
SSS Postulate
SAS Postulate
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…
corresponding angles
If two parallel lines are cut by a transversal, then correspo…
congruent corresponding angles
If two lines are cut by a transversal and corresponding angle…
121 terms
Geometry Postulates, Theorems, and Definitions
Segment Addition Postulate
Protractor Postulate
Parallel Lines
Skew Lines
AB + BC = AC
Says that you can measure any angle
two lines that don't intersect and are coplanar
two lines that don't intersect and aren't coplanar
Segment Addition Postulate
AB + BC = AC
Protractor Postulate
Says that you can measure any angle
16 terms
Geometry Chapter 3 Theorems & Postulates
Parallel Postulate
Perpendicular Postulate
Corresponding Angles Postulate
Alternate Interior Angles Theorem
If there is a line and a point not on the line, then there is…
If there is a line and a point not on the line, then there is…
If two parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the pair…
Parallel Postulate
If there is a line and a point not on the line, then there is…
Perpendicular Postulate
If there is a line and a point not on the line, then there is…
12 terms
Geometry Postulates/ Theorems
Perpendicular Bisector Theorem
Corresponding Angles Theorem
Alternate Interior Angles Theorem
Same-Side Interior Angles Postulate
If a point is on the perpendicular bisector of a segment, the…
If two parallel lines are cut by a transversal, then the pair…
If two parallels are cut by a transversal, then the pair of a…
If two parallel lines are cut by a transversal, then the pair…
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, the…
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the pair…
17 terms
Postulates and Theorems of Geometry 3
Corresponding Angles Postulate (3-1)
Alternate Interior Angles Theorem (3-1)
Consecutive Interior Angles Theorem (3…
Alternate Exterior Angles Theorem (3-3)
If two parallel lines are cut by a transversal, the correspon…
If two parallel lines are cut by a transversal, the alternate…
If two parallel lines are cut by a transversal, the consecuti…
If two parallel lines are cut by a transversal, the alternate…
Corresponding Angles Postulate (3-1)
If two parallel lines are cut by a transversal, the correspon…
Alternate Interior Angles Theorem (3-1)
If two parallel lines are cut by a transversal, the alternate…
62 terms
Geometry Theorems/Postulates/Definitions
theorem
postulate
definition
geometry
a statement that can be proved
something we don't need to prove, uses past information to ba…
assigns a term to an object. are always reversible
to take a series of facts to put in a logical way to reach a…
theorem
a statement that can be proved
postulate
something we don't need to prove, uses past information to ba…
50 terms
Theorems/Postulates/Definition Geometry
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
1. The points on a line can be paired with the real numbers i…
If B is between A and C, then AB+BC=AC
On line AB in a given plane, choose any point O between A and…
If point B lies in the interior of <AOC, the m<AOB a m<BOC =…
Ruler Postulate
1. The points on a line can be paired with the real numbers i…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
31 terms
Geometry Theorems, Postulates, and Properties
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on a line can be matched one to one with the real…
If B is between A and C, then AB+BC=AC.
The measure of ∠AOB, which can be written as m∠AOB, is equal…
If P is in the interior of ∠RST, then the measure of ∠RST is…
Ruler Postulate
The points on a line can be matched one to one with the real…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC.
18 terms
Geometry- Theorems and Postulates
Postulate
Theorem
Intersection of 2 lines is exactly...
Intersection of 2 planes is exactly...
Statement accepted without proof
Conjecture (mathematical hypothesis) that has been proved
1 point
1 line
Postulate
Statement accepted without proof
Theorem
Conjecture (mathematical hypothesis) that has been proved
8 terms
Postulates and Theorems (Geometry)
Corresponding Angles Postulate
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
Consecutive Interior Angles Theorem.
If two parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the pair…
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pair…
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pair…
15 terms
Geometry Postulates and Theorems Chapter 3
Postulate 3-1 Same-side Interior Angle…
Theorem 3-1 Alternate Interior Angles…
Theorem 3-2 Corresponding Angles Theor…
Theorem 3-3 Alternate Exterior Angles…
supplementary... m∠1 + m∠2 = 180
congruent
corresponding
exterior
Postulate 3-1 Same-side Interior Angle…
supplementary... m∠1 + m∠2 = 180
Theorem 3-1 Alternate Interior Angles…
congruent
74 terms
Geometry Definitions, Postulates and Theorems
Complementary angles
Supplementary angles
Theorem
Vertical Angles
two angles whose measures have a sum of 90°
two angles who measures have a sum of 180°
a statement that can be proven
two 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 who measures have a sum of 180°
6 terms
Geometry Chapter 3 - Theorems and Postulates
Parallel Postulate
Perpendicular Postulate
Corresponding Angles Theorem
Alternate Interior Angles Theorem
If there is a line and a point not on the line, then there is…
If there is a line and a point not on the line, then there is…
If two parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the pair…
Parallel Postulate
If there is a line and a point not on the line, then there is…
Perpendicular Postulate
If there is a line and a point not on the line, then there is…
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
27 terms
Geometry Theorems/Postulates
(2-4)Definition of midpoint:
(3-9)Definition of bisector:
(5-2)CPCF Theorem (segment):
(2-4)Definition of a circle:
If a point is the midpoint of a segment, it divides the segme…
If a figure is the the bisector of a segment, it divides the…
If figures are congruent, then corresponding segments are con…
If a figure is a circle, then its radii are congruent. (2-4)
(2-4)Definition of midpoint:
If a point is the midpoint of a segment, it divides the segme…
(3-9)Definition of bisector:
If a figure is the the bisector of a segment, it divides the…
19 terms
Geometry Vocab for the postulates and theorems
parallel pos.
perpendicular pos.
paragraph proof
transitive property of parallel lines
if there is a line and a point not on that line then there is…
if there is a line and a point not on that line then there is…
a proof written as a paragraph
if two lines are parallel to the same line then they are para…
parallel pos.
if there is a line and a point not on that line then there is…
perpendicular pos.
if there is a line and a point not on that line then there is…
64 terms
Geometry Postulates and Theorems
they are congruent.... Right Angles Cong…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Supplem…
they are congruent.... Congruent Complem…
If two angles are right angles, then
If two angles are supplementary to the same angle, then
If two angles are supplementary to congruent angles, then
If two angles are complementary to the same angle, then
they are congruent.... Right Angles Cong…
If two angles are right angles, then
they are congruent.... Congruent Supplem…
If two angles are supplementary to the same angle, then
30 terms
Geometry: postulates, theorems, and definitions
Segment addition postulate
Angle addition postulate
Postulate 5
Postulate 6
If B is between A and C, then AB + BC = AC
If point B lies in the interior of <AOC, then m<AOB + m<BOC =…
A line contains at least two points; a plane contains at leas…
Through any two points there is exactly one line.
Segment addition postulate
If B is between A and C, then AB + BC = AC
Angle addition postulate
If point B lies in the interior of <AOC, then m<AOB + m<BOC =…
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…
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