Study sets matching "honors theorems postulates geometry postulates theorems chapter 9"

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Study sets matching "honors theorems postulates geometry postulates theorems chapter 9"

28 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
15 terms
MCPS Honors Geometry Postulates and Theorems Chapter 3
Same-side Interior Angle Postulate... If…
Alternate Interior Angles Theorem... If a…
Corresponding Angles Theorem... If a tran…
Alternate Exterior Angles Theorem... If a…
supplementary... m∠1 + m∠2 = 180
congruent
corresponding
exterior
Same-side Interior Angle Postulate... If…
supplementary... m∠1 + m∠2 = 180
Alternate Interior Angles Theorem... If a…
congruent
18 terms
Geometry: Chapter 9 Postulates and Theorems
Theorem 9-1
Corollary to Theorem 9-1
Theorem 9-2 (converse of theorem 9-1)
Arc Addition Postulate
If a line is tangent to a circle, then it is perpendicular to…
Tangent segments to a circle from an external point are congr…
If a line is perpendicular to a radius at its outer endpoint,…
One arc plus another arc will equal the total value of the tw…
Theorem 9-1
If a line is tangent to a circle, then it is perpendicular to…
Corollary to Theorem 9-1
Tangent segments to a circle from an external point are congr…
Honors Geometry Postulates and Theorems
Postulate 5
Postulate 6
Postulate 7
Postulate 8
(1) A line contains at least two points (2) A plane contains…
Through any two points there is exactly one line.
(1) Through any three points there is at least one plane (2)…
If two points are in a plane, then the line that contains the…
Postulate 5
(1) A line contains at least two points (2) A plane contains…
Postulate 6
Through any two points there is exactly one line.
Geometry honors theorems and postulates
Midpoint definition
Segment bisector definition
Congruent segments definition
Angle addition postulate
A point that divides the segment into two congruent segments
a point, line, ray, or other segment that intersects a segmen…
Segments that have the same length
Two little angles make one big angle
Midpoint definition
A point that divides the segment into two congruent segments
Segment bisector definition
a point, line, ray, or other segment that intersects a segmen…
31 terms
Geometry Honors Postulates and Theorems
Postulate 1-1-1
Postulate 1-1-2
Postulate 1-1-3
Postulate 1-1-4
Through any two points there is exactly one line
Through any three noncollinear points there is exactly one pl…
If two points lie in a plane, then the line containing those…
If two lines intersect, then they intersect in exactly one po…
Postulate 1-1-1
Through any two points there is exactly one line
Postulate 1-1-2
Through any three noncollinear points there is exactly one pl…
48 terms
Honors Geometry Postulates and Theorems
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The points on a line can be matched one to one with real numb…
If B is between A and C, then AB+BC=AC
Consider OB and a point A on one side of OB. The rays of the…
If P is the interior of angleRST, then the measure of angleRS…
Ruler Postulate
The points on a line can be matched one to one with real numb…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
Honors Geometry Chapter 7 Postulates and Theorems
Theorem 7-1: SAS Similarity Theorem
Theorem 7-2: SSS Similarity Theorem
Theorem 7-3: Triangle Proportionality…
Theorem 7-4: Triangle Angle-Bisector T…
If an angle of one triangle is congruent to an angle of anoth…
If the sides of two triangles are in proportion, then the tri…
If a line parallel to one side of triangle intersects the oth…
If a ray bisects an angle of a triangle, then it divides the…
Theorem 7-1: SAS Similarity Theorem
If an angle of one triangle is congruent to an angle of anoth…
Theorem 7-2: SSS Similarity Theorem
If the sides of two triangles are in proportion, then the tri…
11 terms
geometry - chapter 9 postulates and theorems
* theorem 9-1 *
* corollary to theorem 9-1 *
* theorem 9-2 *
** postulate 16 : arc addition postula…
if a line is tangent to a circle , then the line is perpendic…
tangents to a circle from a point are congruent
if a line of a circle is perpendicular to the radius at its o…
the measure of the arc formed by 2 adjacent arcs is the sum o…
* theorem 9-1 *
if a line is tangent to a circle , then the line is perpendic…
* corollary to theorem 9-1 *
tangents to a circle from a point are congruent
Geometry chapter 9 theorems and postulates
If a line is tangent to a circle then…
Tangents to a circle from one point are
If a line in the plane of a circle is…
The measure of the arc formed by two a…
Perpendicular to the radius drawn to the point of tangency
Congruent
Tangent to the circle
The sum of the measures of these two arcs (arc addition postu…
If a line is tangent to a circle then…
Perpendicular to the radius drawn to the point of tangency
Tangents to a circle from one point are
Congruent
Honors Geometry Postulates/Theorems
postulate 1-1
postulate 1-2
postulate 1-3
postulate 1-4
through any 2 points there is exactly 1 line
if 2 distinct lines intersect, then they intersect in exactly…
if 2 distinct planes intersect, then they intersect in exactl…
through any three non-collinear points there is exactly 1 plane
postulate 1-1
through any 2 points there is exactly 1 line
postulate 1-2
if 2 distinct lines intersect, then they intersect in exactly…
44 terms
GEOMETRY HONORS MIDTERM THEOREMS & POSTULATES
Through any two points there is exactl…
Through any three noncollinear points…
If two points lie in a plane, then the…
If two lines intersect, they then inte…
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, they then intersect at exactly one po…
Through any two points there is exactl…
Through any two points there is exactly one line
Through any three noncollinear points…
Through any three noncollinear points there is exactly one pl…
64 terms
Geometry Honors Theorems & Postulates
2 point, 1 line postulate
3 nonconllinear points, 1 plane postul…
segment addition postulate
angle addition postulate
through any two points, there exists only one line
through any three points not on one line, there exists only o…
AB+BC=AC... if AB+BC=AC, then B lies between A and C
m angle XYZ= m angle XYW+ m angle WYZ
2 point, 1 line postulate
through any two points, there exists only one line
3 nonconllinear points, 1 plane postul…
through any three points not on one line, there exists only o…
17 terms
Honors Geometry Postulates and Theorems
Largest Angle Theorem
Longest side theorem
Vertical angles theorem
Congruent supplements or complements t…
If two sides of a triangle are not congruent then the larger…
if two angles of a triangle are not congruent then the longer…
vertical angles are congruent
if two angles are supplements or complements of the same angl…
Largest Angle Theorem
If two sides of a triangle are not congruent then the larger…
Longest side theorem
if two angles of a triangle are not congruent then the longer…
14 terms
Honors Geometry Definitions, Theorems, Postulates
Midpoint
Supplementary Angles
Perpendicular Lines
Congruent Angles
The point that divides, or bisects, a segment into two congru…
Two angles whose measures have the sum of 180 degrees
Two lines that intersect to form a right angle
Angles that have the same measure
Midpoint
The point that divides, or bisects, a segment into two congru…
Supplementary Angles
Two angles whose measures have the sum of 180 degrees
52 terms
Geometry Honors Postulates & Theorems
Segment Addition Postulate
Angle Addition Postulate
Two Point Postulate
Line-Point Postulate
If B is between A and C, then AB + BC = AC. If AB + BC = AC,…
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 + BC = AC. If AB + BC = AC,…
Angle Addition Postulate
If P is in the interior of angle RST, then the measure of ang…
Honors Geometry Theorems/Postulates
If two angles are supplementary to the…
If two angles form a linear pair, then…
If two angles are complementary to the…
All right angles are congurent
Congruent Supplements Theorem
Linear Pair Theorem
Congruent Complements Theorem
Right Angle Congruence Theorem
If two angles are supplementary to the…
Congruent Supplements Theorem
If two angles form a linear pair, then…
Linear Pair Theorem
14 terms
Honors Geometry: Theorems/Postulates
Complementary Angles
Congruent Angles
Congruent Complements Theorem
Congruent Segments
Two angles whose measures have the sum of 90 degrees.
Angles that have the same measure.
If two angles are complementary to the same angle or to congr…
Segments that have the same length.
Complementary Angles
Two angles whose measures have the sum of 90 degrees.
Congruent Angles
Angles that have the same measure.
32 terms
Geometry Honors Theorems and Postulates
theorem 1
theorem 2
theorem 3
theorem 4
If two angles are right angles, then they are congruent
if two angles are straight angles, then they are congruent
If a conditional statement is true, the the contrapositive of…
If angles are supplementary to the same angle, then they are…
theorem 1
If two angles are right angles, then they are congruent
theorem 2
if two angles are straight angles, then they are congruent
Honors Geometry Postulates and Theorems
Through any two points
If two lines intersect then
If two distinct planes intersect then
Through any 3 non-collinear points
There is exactly one line.
They intersect at exactly one point.
They intersect at exactly one line.
There is one plane.
Through any two points
There is exactly one line.
If two lines intersect then
They intersect at exactly one point.
27 terms
Honors Geometry Theorems and Postulates
Postulate
Ruler Postulate
Congruent Segments
Segment Addition Postulate
A subject we accept as being true without truly proving it
You can find the distance between any two point on a line.
Two segments that have the same length
If B is between A and C, then AB + BC = AC
Postulate
A subject we accept as being true without truly proving it
Ruler Postulate
You can find the distance between any two point on a line.
120 terms
Honors Geometry Postulates and Theorems
Linear Pair Postulate
vertical angles theorem
Protractor Postulate
Angle Addition Postulate
if 2 angles form a linear pair, then they are supplementary
vertical angles are congruent
every angles has a degree measure that can be measured with a…
if B is the interior of /_ AOC then m/_AOB + m/_BOC = /_AOC
Linear Pair Postulate
if 2 angles form a linear pair, then they are supplementary
vertical angles theorem
vertical angles are congruent
Honors Geometry: Theorems and Postulates
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Every line segment has a length that can be measured with a r…
If B is between A and C, then AB+BC=AC
Every angle has a degree measure that can be measured with a…
If B is in the interior of <RST, then m<RST=m<RSP+m<PST
Ruler Postulate
Every line segment has a length that can be measured with a r…
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
Honors geometry theorems and postulates
Perpendicular bisector theorem
Consecutive interior angles postulate
Alternate interior angles theorem
Alternate exterior angles theorem
If a point is on the perpendicular bisector of a segment, the…
If two parallel lines are cut by a transversal, then each pai…
If two parallel lines are cut by a transversal, then each pai…
If two parallel lines are cut by a transversal, the. Each pai…
Perpendicular bisector theorem
If a point is on the perpendicular bisector of a segment, the…
Consecutive interior angles postulate
If two parallel lines are cut by a transversal, then each pai…
Honors Geometry(postulates and theorems)
Segment addiction postulate
Angle addition postulate
Supplement theorem
Complement theorem
If A, B, and C are collinear, then point B is between A and C…
D is in the interior of <ABC if and only if m<ABD + m<DBC = m…
If two angles form a linear pair, then they are supplementary…
If the non common sides of two adjacent angles form a right a…
Segment addiction postulate
If A, B, and C are collinear, then point B is between A and C…
Angle addition postulate
D is in the interior of <ABC if and only if m<ABD + m<DBC = m…
Postulates and Theorems - Honors Geometry
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.
On line AB in a given plane, choose any point O between A and…
If point B lies in the interior of angle AOC, then the measur…
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.
Geometry Chapter 9 Postulates and Theorems
Biconditional Tangent Perpendicular to…
The two tangents to a circle from a po…
Arc Addition Postulate
Congruent minor arcs <=> congruent cen…
A line is tangent to a circle, if and only if the line is per…
...are congruent.
The measure of the arc formed by two adjacent arcs is the sum…
In the same circle or in congruent circles, two minor arcs ar…
Biconditional Tangent Perpendicular to…
A line is tangent to a circle, if and only if the line is per…
The two tangents to a circle from a po…
...are congruent.
17 terms
Honors Geometry Theorems and Postulates
Through any two points there is exactl…
If two line intersect, then they inter…
If two planes intersect, their interse…
Through any 3 noncollinear points ther…
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points there is exactl…
Postulate 1-1
If two line intersect, then they inter…
Postulate 1-2
Honors Geometry Postulates and Theorems
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 and j=k, then a+j=b+k
If a=b, then a-c=b-c... If a=b and j=k, then a-j=b-k
If a=b, then wa=wb... if c=d and r=s, then cr=ds
If p=q, then p/q=q/p
Addition Property Of Equality
If a=b, then a+c=b+c... If a=b and j=k, then a+j=b+k
Subtraction Property of Equality
If a=b, then a-c=b-c... If a=b and j=k, then a-j=b-k
12 terms
Geometry Honors Postulates and Theorems
Angle Addition Postulate
Segment Addition Postulate
Ruler Postulate
Protractor Postulates
2 adjacent angles = a whole; angle abc + cbd = abd
Segment 1 + Segment 2 = the Whole; ab+bc=ac
Points on a number line can be matched up with real numbers
Rays can be matched with real numbers
Angle Addition Postulate
2 adjacent angles = a whole; angle abc + cbd = abd
Segment Addition Postulate
Segment 1 + Segment 2 = the Whole; ab+bc=ac
21 terms
Honors Geometry Chapter 4 Definitions, Postulates, and Theorems
Acute Triangle
Obtuse Triangle
Right Triangle
Equiangular Triangle
Three acute angles
One obtuse angle
One right angle
Three congruent angles
Acute Triangle
Three acute angles
Obtuse Triangle
One obtuse angle
43 terms
Postulates & Theorems - Geometry Honors 2015
Postulate 2
Postulate 4
Postulate 5
Postulate 6
Segment addition postulate
The whole of an angle is the sum of its parts - Angle additio…
A line contains at least 2 points; a plane contains at least…
through any two points there is exactly one line
Postulate 2
Segment addition postulate
Postulate 4
The whole of an angle is the sum of its parts - Angle additio…
29 terms
Honors Geometry Postulates and Theorems
Same-Side Interior Angles POSTULATE
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
Corresponding Angles Theorem
If a transversal intersects two parallel lines then the same-…
If a transversal intersects two parallel lines then alternate…
If a transversal intersects two parallel lines then alternate…
If a transversal intersects two parallel lines then correspon…
Same-Side Interior Angles POSTULATE
If a transversal intersects two parallel lines then the same-…
Alternate Interior Angles Theorem
If a transversal intersects two parallel lines then alternate…
57 terms
Honors geometry theorems and postulates
Reflexive property
Sss
Sas
Asa
Anything congruent to itself
Side side side
Side angle side
Angle side angle
Reflexive property
Anything congruent to itself
Sss
Side side side
Honors Geometry - Chapter 1 Postulates & Theorems
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Through any two points there is exactly one line.
If two lines intersect, then they intersect in exactly one po…
If two plains intersect, then they intersect in exactly one l…
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 lines intersect, then they intersect in exactly one po…
Honors Geometry Chapter 6 Postulates and Theorems
Theorem 6-1: The Exterior Angle Theorem
Theorem 6-2
Theorem 6-3
Corollary 1
The measure of an exterior angle of a triangle is greater tha…
If one side of a triangle is longer than a second side, then…
If one angle of a triangle is larger than a second angle, the…
The perpendicular segment from a point to a line is the short…
Theorem 6-1: The Exterior Angle Theorem
The measure of an exterior angle of a triangle is greater tha…
Theorem 6-2
If one side of a triangle is longer than a second side, then…
19 terms
Geometry Chapter 9 Theorems/Postulate
Congruent Circles Theorem
Similar Circles Theorem
Tangent Segments Theorem
Secant Segments Theorem
Two or more circles are congruent if they have the same radiu…
All circles are similar
If two tangents intersect outside of a circle, they are congr…
If two secants intersect outside of a circle, then the produc…
Congruent Circles Theorem
Two or more circles are congruent if they have the same radiu…
Similar Circles Theorem
All circles are similar
17 terms
Geometry Honors Postulates & Theorems
Postulate 1-1-1
Postulate 1-1-2
Postulate 1-1-3
Postulate 1-1-4
Through any two points there is exactly one line.
Through any three noncollinear points there is exactly one pl…
If two points lie in a plane, then the line containing those…
If two lines intersect, then they intersect 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…
Honors Geometry - Chapter 2 Postulates & Theorems
Law of Detachment
Law of Syllogism
Properties of Congruence
Vertical Angles Theorem
If a conditional is true and its hypothesis is true, then its…
If p→q and q→r are true statements, then p→r is a true statem…
Reflexive Property: AB≅AB and ∠A≅∠A. Symmetric Property: If A…
Vertical angles are congruent.
Law of Detachment
If a conditional is true and its hypothesis is true, then its…
Law of Syllogism
If p→q and q→r are true statements, then p→r is a true statem…
Geometry Honors - Chapter 3 Theorems/Postulates/Definitions
Parallel Lines (||)
Parallel Planes
Skew
Transversal
2 lines that never intersect
2 planes that never intersect
lines which are not coplanar and do not intersect
a line which intersects 2 or more lines
Parallel Lines (||)
2 lines that never intersect
Parallel Planes
2 planes that never intersect
Honors Geometry - Chapter 3 Postulates & Theorems
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 alternat…
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 alternat…
Geometry Honors - Chapter 1 Theorems/Postulates/Definitions
Point
Line
Planes
Collinear
describe a location, no size (labeled with Capital Letters)
go on in both directions forever, infinite points on a line,…
infinite number of points contained, flat 2D, 3 points minimu…
All the points lie on same line
Point
describe a location, no size (labeled with Capital Letters)
Line
go on in both directions forever, infinite points on a line,…
Lowell Honors Geometry Postulates and Theorems
Distance Postulate
Ruler Postulate
Ruler Placement Postulate
Line Postulate
To every pair of different points there corresponds a unique…
The points of a line can be placed in correspondence with the…
Given two points P and Q of a line, the coordinate system can…
For every two different points there is exactly one line that…
Distance Postulate
To every pair of different points there corresponds a unique…
Ruler Postulate
The points of a line can be placed in correspondence with the…
83 terms
Honors Geometry - Final (Postulates/Theorems)
Through any two points...
Through any three noncollinear points...
A line consists of...
A plane contains at least...
there is exactly one line
there is exactly one plane
a least 2 points
3 noncollinear points
Through any two points...
there is exactly one line
Through any three noncollinear points...
there is exactly one plane
Geometry Honors - Chapter 2 Theorems/Postulates/Definitions
Inductive Reasoning
Conjecture
Counterexample
Statement
logic used to reach a conclusion or conjecture
A conclusion that is maybe true or false
example that shows that a conjecture is false
a sentence that can be either True or False
Inductive Reasoning
logic used to reach a conclusion or conjecture
Conjecture
A conclusion that is maybe true or false
30 terms
Honors 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 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…
14 terms
geometry honors - postulates and theorems
Corresponding Angles Postulate
Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem
Same Side 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 two…
If two parallel lines are cut by a transversal, then the two…
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…
Honors Geometry Theorems & Postulates Chapter 2
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 angle PQR, then m<PQS + m<SQR = m<…
a2 + b2 = c2
If 2 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 angle PQR, then m<PQS + m<SQR = m<…
Theorems and Postulates- Honors Geometry
SSS Postulate (Side-side-side)
SAS Postulate (side-angle-side)
ASA Postulate (angle-side-angle
AAS Postulate (angle-angle-side)
If all three sides of one triangle are congruent to all 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…
If two angles and a non-included side of one triangle are con…
SSS Postulate (Side-side-side)
If all three sides of one triangle are congruent to all three…
SAS Postulate (side-angle-side)
If two sides and the included angle of one triangle are congr…
10 terms
Geometry Theorems, Postulates, and Definitions, Chapter 9
The Area Postulate
Postulate 9
Corollary to Postulate 9
Theorem 38
Every polygonal region has a positive number called its area…
The area of a rectangle is the product of its base and altitu…
The area of a square is the square of its side
The area of a right triangle is half the product of its legs
The Area Postulate
Every polygonal region has a positive number called its area…
Postulate 9
The area of a rectangle is the product of its base and altitu…
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