Study sets matching "honors theorems postulates geometry postulates theorems"

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Study sets matching "honors theorems postulates geometry postulates theorems"

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
Geometry Theorems/Postulates
AAA Similarity Polstulate
SAS Similarity Theorem
SSS Similarity Theorem
Triangle Proportionality Theorem
If two angles of one triangle are congruent to two angles of…
If an angle of one triangle is congruent to an angle of anthe…
If the corresponding sides of two triangles are in proportion…
If a line parallel to a side of a triangle intersects the oth…
AAA Similarity Polstulate
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 anthe…
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
49 terms
Geometry Theorems & Postulates
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points, there is exactly one line.
Lines can only intersect at exactly one point.
Planes can only intersect at exactly one line.
Through any three non-collinear points, there is exactly one…
Postulate 1-1
Through any two points, there is exactly one line.
Postulate 1-2
Lines can only intersect at exactly one point.
23 terms
geometry exam~postulates and theorems
right angles congruence theorem
congruent supplements theorem
congruent complements theorem
linear pairs 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…
Geometry Theorems and Postulates
the parallel postulate
theorem 16
theorem 17
corollary to theorem 17 : 1
through a point not on a line, there is exactly one line para…
in a plane, two points each equidistant from the endpoints of…
equal corresponding angles mean lines are parallel
equal alternate interior angles mean lines are parallel
the parallel postulate
through a point not on a line, there is exactly one line para…
theorem 16
in a plane, two points each equidistant from the endpoints of…
37 terms
Geometry Test Theorems and Postulates
Linear Pair Theorem
Congruent Supplements Theorem
Right Angle Congruence Theorem
Congruent Complements Theorem
If 2 angles form a linear pair, then they are supplementary
If 2 angles are supplements of congruent angles or the same a…
If 2 angles are right angles then they are congruent
if two angles are complementary to the same angle or congruen…
Linear Pair Theorem
If 2 angles form a linear pair, then they are supplementary
Congruent Supplements Theorem
If 2 angles are supplements of congruent angles or the same a…
Geometry Postulates and Theorems
they are congruent.... Right Angles Cong…
Congruent Supplements Theorem
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 they…
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
Congruent Supplements Theorem
If two angles are supplementary to the same angle, then they…
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…
Postulates & Theorems-Honors Groden
Postulate "#5"
Postulate "#6"
Postulate "#7"
Postulate "#8"
A line contains at least 2 points.... A plane contains at least…
Through any two points there is exactly one line.
Through any three points there is at least one plane.... Through…
If two points are in a plane, the line that contains those po…
Postulate "#5"
A line contains at least 2 points.... A plane contains at least…
Postulate "#6"
Through any two points there is exactly one line.
Geometry Honors - Chapter 4 Theorems/Postulates/Corollaries
Theorem 4.1 (Angle Sum Theorem)
Theorem 4.2 (Exterior Angles Theorem)
Corollary 4.1
Corollary 4.2
all three angles of a triangle equal 180 degrees
The exterior angle is equal to the sum of the 2 remote interi…
In a right triangle, the 2 acute angles are complementary
A triangle can have at most one right angle or one obtuse angle
Theorem 4.1 (Angle Sum Theorem)
all three angles of a triangle equal 180 degrees
Theorem 4.2 (Exterior Angles Theorem)
The exterior angle is equal to the sum of the 2 remote interi…
11 terms
Geometry Triangle Theorems and Postulates
Isosceles Triangle Theorem
Converse to Isosceles Triangle Theorem
SSS postulate
SAS postulate
If two sides of a triangle are congruent, then the angles opp…
If two angles of a triangle are congruent, then the sides opp…
If three sides of one triangle are congruent to three sides o…
If two sides and the included angle of one triangle are congr…
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opp…
Converse to Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opp…
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
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
59 terms
Geometry Postulates, Theorems, and Properties
Addition Property 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 ac = bc.
If a = b and c ≠ 0, then a/c = b/c.
Addition Property of Equality
If a = b, then a + c = b + c.
Subtraction Property of Equality
If a = b, then a - c = b - c.
126 terms
Geometry Honors chapter 1-3 vocab,Theorems, postulates
Math
Geometry
Conjecture
Inductive reasoning
The Science of patterns
The science of visual patterns
An unproven statement based on observations
A reasoning process that involved looking for patterns and ma…
Math
The Science of patterns
Geometry
The science of visual patterns
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
Saxon Geometry: Theorems and Postulates
Postulate 1: Ruler Postulate
Postulate 2: Segment Addition Postulate
Postulate 4: The Angle Addition Postul…
Postulate 5
The points on a line can be paired in a one-to-one correspond…
If B is between A and C, then AB + BC = AC
If point D is in the interior of angle ABC, then the m of ang…
Through any two points there is exactly one line.
Postulate 1: Ruler Postulate
The points on a line can be paired in a one-to-one correspond…
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB + BC = AC
13 terms
Geometry Honors Chapter 4 Terms, Postulates, and Theorems
Polygons whose corresponding parts are…
The same or equal.
If two angles of one triangle are cong…
If three sides of one triangle are con…
Congruent Polygons
Congruent
Triangle Third Angle Sum Theorem
SSS Congruence Postulate
Polygons whose corresponding parts are…
Congruent Polygons
The same or equal.
Congruent
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…
14 terms
Geometry honors unit 5 theorems and postulates
What are the five ways to prove a shap…
If two lines are parallel
If three parallel lines cut off congru…
A line that contains the midpoint of o…
1.) if both pairs of opposite sides of a quadrilateral are co…
then all the points on one line are equidistant from the othe…
then they cut off congruent segments on every transversal
passes through the midpoint of the third side
What are the five ways to prove a shap…
1.) if both pairs of opposite sides of a quadrilateral are co…
If two lines are parallel
then all the points on one line are equidistant from the othe…
Honors Geometry Definitions, Postulates, Theorems & Equations
Point
Line
plane
Co-linear points
a location in space
an infinite set of points strung together in one dimension
an infinite set of points strung together to form a boundless…
points that lie on the same line
Point
a location in space
Line
an infinite set of points strung together in one dimension
21 terms
Geometry I Postulates and Theorems
Through any two points there is exactl…
Through any three points there is at l…
If two lines intersect, then they inte…
If two planes intersect, then their in…
...
...
...
...
Through any two points there is exactl…
...
Through any three points there is at l…
...
10 terms
Geometry Honors Chapter 1: Postulates and Theorems
Dimension Postulate
Straight Line Postulate
Plane Existence Postulate
Flat Plane Postulate
A line contains at least 2 points... A plane contains at least 3…
Through any 2 distinct points there is exactly 1 line... 2 disti…
Through any 3 points there is at least 1 plane... 3 noncollinear…
If 2 points are in a plane, then the line that contains them…
Dimension Postulate
A line contains at least 2 points... A plane contains at least 3…
Straight Line Postulate
Through any 2 distinct points there is exactly 1 line... 2 disti…
33 terms
Geometry A Theorems and postulates
Segment Addition Postulate
Supplement Theorem
Complement Theorem
Congruent Complements theorem
If B is between A and C, then AB+BC=AC
if 2 angles form a linear pair, then they are supplementary a…
If the noncommon sides of 2 adjacent angles form a right angl…
if <1+<2=180 and <2+<3=180, then <1 congruent to <3
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
Supplement Theorem
if 2 angles form a linear pair, then they are supplementary a…
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
93 terms
GEOMETRY FORMULAS, THEOREMS, AND POSTULATES
Slope-Intercept Form of a line
Slope formula
Positive slope
Negative slope
Slope-Intercept Form of a line
Slope formula
35 terms
Geometry Theorems, Postulates, and Properties
Addition property 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 and c≠0, then a/c=b/c
Addition property of equality
If a=b, then a+c=b+c
Subtraction property of equality
If a=b, then a-c=b-c
23 terms
Geometry Honors Definitions, theorems, postulates, etc.
Point
Line
Plane
Collinear Points
A location in space
An infinite set of points strung together in one dimension
An infinite set of points strung together to form a boundless…
Points that lie on the same line
Point
A location in space
Line
An infinite set of points strung together in one dimension
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…
28 terms
Geometry Honors 7-12 Theorems and Postulates
If c^2=a^2=b^2, then the triangle is a…
A=½h(b₁=b₂)
The measure of the arc formed by two a…
Length of ArcAB=mArcAB/360*2πr
Converse of the Pythagorean Theorem
Area of a Trapezoid
Arc Addition Postulate
Arc Length
If c^2=a^2=b^2, then the triangle is a…
Converse of the Pythagorean Theorem
A=½h(b₁=b₂)
Area of a Trapezoid
Geometry Postulates and Theorems 2
Conditional
Converse
Inverse
Contrapositive
p→q; if p then q; equivalent to Contrapositive
q→p; if q then p; equivalent to Inverse
~p→~q; if not p then not q; equivalent to Converse
~q→~p; if not q then not p; equivalent to Conditional
Conditional
p→q; if p then q; equivalent to Contrapositive
Converse
q→p; if q then p; equivalent to Inverse
49 terms
Honors Geometry Postulates, Theorems and Vocab test
A(n) _________ is the part of a line c…
Two segments with the same lengths are…
A(n) __________ of a segment is the po…
A(n) __________ is a ray that divides…
segment
congruent
midpoint
angle bisector
A(n) _________ is the part of a line c…
segment
Two segments with the same lengths are…
congruent
34 terms
Geometry 210 Postulates and Theorems
Undefined Terms
Segment AB
Ray AB
The Line Postulate
Points, Lines, and Planes
Consists of points A and B and all the points in between them
Consists of segment AB and all points C such that B is betwee…
Through any two points there is exactly one line
Undefined Terms
Points, Lines, and Planes
Segment AB
Consists of points A and B and all the points in between them
37 terms
Geometry Honors - Chapter 6 Theorems/Postulates/Defintions
Theorem 6.1 (Sum of Interior Angles of…
Theorem 6.2 (Sum of Exterior Angles of…
Theorem 6.3
Theorem 6.4
The sum of the interior angles of a convex polygon is represe…
The sum of the exterior angles of a convex polygon will alway…
Opposite sides of a parallelogram are congruent
Opposite angles of a parallelogram are congruent
Theorem 6.1 (Sum of Interior Angles of…
The sum of the interior angles of a convex polygon is represe…
Theorem 6.2 (Sum of Exterior Angles of…
The sum of the exterior angles of a convex polygon will alway…
12 terms
Honors Geometry Postulates and Theorems Ch. 3
The Ruler Postulate
The Protractor Postulate
The Betweenness of Points Theorem
The Betweenness of Rays Theorem
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…
If A-B-C, then AB+BC=AC
If OA-OB-OC, then aAOB+aBOC=aAOC
The Ruler Postulate
The points on a line can be numbered so that positive number…
The Protractor Postulate
The rays in a half rotation can be numbered from 0 to 180 so…
24 terms
Honors Geometry Postulates, Properties, Theorems, & Laws.
law of detachment
law of syllogism
postulate 5
postulate 6
if P implies Q is a true conditional statement and P is true,…
if P implies Q and Q implies R is true, then P implies R.
through any two points there exists exactly one line.
a line contains at least two points.
law of detachment
if P implies Q is a true conditional statement and P is true,…
law of syllogism
if P implies Q and Q implies R is true, then P implies R.
39 terms
Geometry Honors Final--Definitions, Postulates, and Theorems
Definition of right angles
Definition of straight angles
Definition of congruent angles
If 2 angles are right
If an angle is right, it is 90 degrees
If an angle is straight, it is 180 degrees
If 2 angles have the same measure, then they are congruent
then they are congruent
Definition of right angles
If an angle is right, it is 90 degrees
Definition of straight angles
If an angle is straight, it is 180 degrees
Geometry H Midterm (Theorems and Postulates)
segment addition postulate
angle addition postulate
Post. 5: A line contains at least ____…
Post 5: A plane contains at least ____…
ex: If B is between points A and C then AB + BC = AC (pieces…
ex: if point B lies in the interior of <AOC then m<AOB + <BOC…
two
three
segment addition postulate
ex: If B is between points A and C then AB + BC = AC (pieces…
angle addition postulate
ex: if point B lies in the interior of <AOC then m<AOB + <BOC…
47 terms
Geometry Theorems, Properties, and Postulates
Addition Property 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, c not equal to "zero", then a/c = b/c
Addition Property of Equality
If a = b, then a + c = b + c
Subtraction Property of Equality
If a = b, then a - c = b - c
Honors Geometry: Definitions, Postulates, Properties, and Theorems
Segment Addition Postulate
AM + MB = AB
Definition of a Midpoint
If M is the midpoint of AB, then AM = MB
AM + MB = AB
Segment Addition Postulate
If M is the midpoint of AB, then AM = MB
Definition of a Midpoint
Segment Addition Postulate
AM + MB = AB
AM + MB = AB
Segment Addition Postulate
185 terms
Honors Geometry Defintions, Theorems, Postulates, and Properties
point
Line
Plane
Collinear
represents a particular location. That which has no part.
an infinite collection of points in one dimension- that which…
an infinite collection in two dimension - that which has leng…
3 Points are collinear iff they are on the same line
point
represents a particular location. That which has no part.
Line
an infinite collection of points in one dimension- that which…
Triangles - Theorems and Postulates for Geometry
Side-Side-Side (SSS) Congruence
Side-Angle-Side (SAS) Congruence
Angle-Side-Angle (ASA) Congruence
Angle-Angle-Side (AAS) Congruence
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 included side of one triangle are congr…
If two angles and the non-included side of one triangle are c…
Side-Side-Side (SSS) Congruence
If three sides of one triangle are congruent to three sides o…
Side-Angle-Side (SAS) Congruence
If two sides and the included angle of one triangle are congr…
Parallels- Theorems and Postulates for Geometry
Corresponding Angles
Corresponding Angles Converse
Alternate Interior Angles
Alternate Exterior Angles
If two parallel lines are cut by a transversal, then the pair…
If two lines are cut by a transversal and the corresponding a…
If two parallel lines are cut by a transversal, then the alte…
If two parallel lines are cut by a transversal, then the alte…
Corresponding Angles
If two parallel lines are cut by a transversal, then the pair…
Corresponding Angles Converse
If two lines are cut by a transversal and the corresponding a…
Circles - Theorems and Postulates for Geometry
Radius
Chords
Tangents
Arcs
In a circle, a radius perpendicular to a chord bisects the ch…
In a circle, or congruent circles, congruent chords are equid…
Tangent segments to a circle from the same external point are…
In the same circle, or congruent circles, congruent central a…
Radius
In a circle, a radius perpendicular to a chord bisects the ch…
Chords
In a circle, or congruent circles, congruent chords are equid…
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…
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…
Theorems and postulates for geometry
Reflexive property
Symmetric property
Transitive property
Addition postulate
A quantity is congruent to itself
If a=b then b=a
If a=b and b=c then a=c
If equal quantities are added to equal quantities the sums ar…
Reflexive property
A quantity is congruent to itself
Symmetric property
If a=b then b=a
Quadrilaterals-Theorems and Postulates for Geometry
Parallelograms- About Sides
Parallelograms- About Angles
Parallelograms- About Diagonals
Parallelogram Converses- About Sides
If a quadrilateral is a parallelogram, the opposite... sides ar…
* If a quadrilateral is a parallelogram, the opposite... angles…
* If a quadrilateral is a parallelogram, the diagonals... bisec…
* If both pairs of opposite sides of a quadrilateral... are par…
Parallelograms- About Sides
If a quadrilateral is a parallelogram, the opposite... sides ar…
Parallelograms- About Angles
* If a quadrilateral is a parallelogram, the opposite... angles…
69 terms
Postulates, Theorems, Definitions and Properties- Honors Geometry
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Line Postulate
If point B is between points 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 the m∠AOB and t…
A line contains at least 2 points
Segment Addition Postulate
If point B is between points A and C, then AB+BC=AC
Protractor Postulate
On line AB in a given plane, choose any point O between A and…
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