# Study sets matching "geometry theorems etc"

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Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

Vertical Angles Congruence Theorem

If B is between A and C, then AB + BC = AC. ... If AB + BC = AC,…

If B is in the interior of ∠AOC, then the measure of ∠AOC is e…

If two angles form a linear pair, then they are supplementary.…

Vertical angles are congruent ... ∠A ≅ ∠B

Segment Addition Postulate

If B is between A and C, then AB + BC = AC. ... If AB + BC = AC,…

Angle Addition Postulate

If B is in the interior of ∠AOC, then the measure of ∠AOC is e…

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Law of Detachment

Let A, B, and C be collinear points. If B is between A and C,…

Given line AB and a point O on line AB, all rays that can be d…

If B is in the interior of <AOC, then the m<AOB + m<BOC = m<AOC

if p->q is a true conditional statement, and p is true, then q…

Segment Addition Postulate

Let A, B, and C be collinear points. If B is between A and C,…

Protractor Postulate

Given line AB and a point O on line AB, all rays that can be d…

Addition Property of Equality

Multiplication Property of Equality

Division Property of Equality

Substitution Property

If a = b, then a + c = b + c

if a = b, then ac = bc

If a = b, then either may be substituted for the other

Addition Property of Equality

If a = b, then a + c = b + c

Multiplication Property of Equality

if a = b, then ac = bc

undefined term

point

line

plane

a word without a formal definition

undefined, a location with no size or dimension

undefined, a series of infinite points that extends in two dir…

undefined, flat surface that has no thickness and extends in a…

undefined term

a word without a formal definition

point

undefined, a location with no size or dimension

The Trichotomy ("Three Possibilities")…

The Transitive Property

The Addition Property of Inequality

The Multiplication Property of Inequali…

Either a>b, a=b, or a<b

If a>b and b>c, then a>c

If a>b, then a+c>b+c

If a>b and c>0, then ac>bc

The Trichotomy ("Three Possibilities")…

Either a>b, a=b, or a<b

The Transitive Property

If a>b and b>c, then a>c

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Law of Detachment

Let A, B, and C be collinear points. If B is between A and C,…

Given line AB and a point O on line AB, all rays that can be d…

If B is in the interior of <AOC, then the m<AOB + m<BOC = m<AOC

if p->q is a true conditional statement, and p is true, then q…

Segment Addition Postulate

Let A, B, and C be collinear points. If B is between A and C,…

Protractor Postulate

Given line AB and a point O on line AB, all rays that can be d…

Linear Pair Theorem

Vertical Angles Theorem

Corresponding Angles Postulate

Two Perps Theorem

If two angles form a linear pair, then they are supplementary.

If two angles are vertical angles, then they are congruent.

If two parallel lines are cut by a transversal, then the pairs…

If two lines are perpendicular to the same line, then the line…

Linear Pair Theorem

If two angles form a linear pair, then they are supplementary.

Vertical Angles Theorem

If two angles are vertical angles, then they are congruent.

The diagonals of a ______ are congruent.

The diagonals of a _______ are perpendi…

Each diagonal of a rhombus _____ two an…

The midpoint of the hypotenuse of a rig…

rectangles,

rhombus

bisects

equidistant

The diagonals of a ______ are congruent.

rectangles,

The diagonals of a _______ are perpendi…

rhombus

Linear Pair Postulate (LPP)

Vertical Angle Theorem (VAT)

Reflexive Property

Transitive Property

two angles that are a linear pair are supplementary

vertical angles are congruent

2 sides of an equation look identical (ex: 5=5)

2 things that are = to a 3rd thing are = to each other

Linear Pair Postulate (LPP)

two angles that are a linear pair are supplementary

Vertical Angle Theorem (VAT)

vertical angles are congruent

Side-Angle-Side (SAS) (Postulate)

Side-Side-Side (SSS) (Postulate)

Angle-Side-Angle (Postulate)

Angle-Angle-Side (AAS) Theorem

If two sides and the included angle of one triangle are congru…

If the three sides of one triangle are congruent to the three…

If two angles and the included side of one triangle are congru…

If two angles and a non include side of one triangle are congr…

Side-Angle-Side (SAS) (Postulate)

If two sides and the included angle of one triangle are congru…

Side-Side-Side (SSS) (Postulate)

If the three sides of one triangle are congruent to the three…

Leg-Leg Congruence

Hypotenuse-Angle Congruence

Leg-Angle Congruence

Hypotenuse-Leg Congruence

If the legs of one right triangle are congruent to the corresp…

If the hypotenuse and acute angle of one right triangle are co…

If one leg and an acute angle of one right triangle are congru…

If the hypotenuse and a leg of one right triangle are congruen…

Leg-Leg Congruence

If the legs of one right triangle are congruent to the corresp…

Hypotenuse-Angle Congruence

If the hypotenuse and acute angle of one right triangle are co…

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

Linear Pair Theorem

Theorem

Congruent supplements theorem

Right angle congruence theorem

If 2 angles form a linear pair, then they are supplementary

A statement that must be proven

If 2 angles are supplementary to the same angle, then the 2 an…

All right angles are congruent

Linear Pair Theorem

If 2 angles form a linear pair, then they are supplementary

Theorem

A statement that must be proven

Same-Side Interiors Angle Postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then same-side…

If a transversal intersects two parallel lines, the alternate…

If a transversal intersects two parallel lines, then correspon…

If a transversal intersects two parallel lines, then alternate…

Same-Side Interiors Angle Postulate

If a transversal intersects two parallel lines, then same-side…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, the alternate…

Addition property

Subtraction property

Multiplication property

Division property

If A=B and C=D, then a+c=b+d

If A=B and C=D, then a-c=b-d

If A=B, then CA=CB

If A=B, then C=0, then a/c=b/c

Addition property

If A=B and C=D, then a+c=b+d

Subtraction property

If A=B and C=D, then a-c=b-d

AA Similarity Postulate

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

If two angles of one triangle are congruent to two other trian…

If an angle of one triangle is congruent to an angle of anothe…

If the sides of two triangles are in proportion, then the tria…

If a line parallel to one side of a triangle intersects the ot…

AA Similarity Postulate

If two angles of one triangle are congruent to two other trian…

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anothe…

addition, subtraction, multiplication,…

definitions, postulates, properties, th…

ruler postulate

segment addition postulate

Properties of Equality

Tools

The points on a line can be matched one to one with real numbe…

If b is between a and c, then ab + bc = ac. If ab + bc = ac th…

addition, subtraction, multiplication,…

Properties of Equality

definitions, postulates, properties, th…

Tools

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If a=b and c=d, then a+c=b+d

If a=b and c=d, then a-c=b-d

If a=b, then ca=cb

If a=b and c≠0, then a÷c=b÷c

Addition Property of Equality

If a=b and c=d, then a+c=b+d

Subtraction Property of Equality

If a=b and c=d, then a-c=b-d

the exterior angle inequality theorem (…

converse (pg.208)

inverse (pg.208)

contrapositive (pg.208)

the measure of an exterior angle of a triangle is greater than…

if q, then p... (if the original statement is: if p, then q)

if not p, then not q ... (if the given statement is: if p, then q)

if not q, then not p... (if the given statement is: if p, then q)

the exterior angle inequality theorem (…

the measure of an exterior angle of a triangle is greater than…

converse (pg.208)

if q, then p... (if the original statement is: if p, then q)

Definition of parallel lines

Definition of skew lines

Definition of parallel planes

If two parallel planes are cut by a thi…

Coplanar lines that do not intersect

Noncoplanar lines; neither parallel or intersecting

Non intersecting planes

The lines of intersection are parallel

Definition of parallel lines

Coplanar lines that do not intersect

Definition of skew lines

Noncoplanar lines; neither parallel or intersecting

Reflexive property of congruence

Symmetric property of congruence

Transitive property of congruence

Linear pair theorem

Figure A ≅ to figure A

If figure A ≅ figure B, then figure B ≅ figure A

If figure A ≅ figure B and figure B ≅ figure C, then figure A…

If ∠ A and ∠ B form a linear pair, ∠ A and ∠ B are supplementa…

Reflexive property of congruence

Figure A ≅ to figure A

Symmetric property of congruence

If figure A ≅ figure B, then figure B ≅ figure A

*Through any two points...

* If two lines intersect...

*If two planes intersect...

*Through any three noncollinear points.…

...there is exactly one line

...then they intersect in exactly one point

...then they intersect in exactly one line

...there is exactly one plane

*Through any two points...

...there is exactly one line

* If two lines intersect...

...then they intersect in exactly one point

Addition Postulate

Subtraction Postulate

Multiplication Postulate

Division Postulate

if a=b and c=d, then a+c = b+d

if a=b and c=d, then a-c = b-d

if a=b, then ac = bc

if a=b and c is not equal to 0, then a/c = b/c

Addition Postulate

if a=b and c=d, then a+c = b+d

Subtraction Postulate

if a=b and c=d, then a-c = b-d

Point (undefined term)

Line (undefined term)

Plane (undefined term)

Collinear points (term)

Indicates a location, has no size

Extends infinitely, has no thickness, contains infinitely many…

Flat surface that extends without end, has no thickness, conta…

Points that lie on the same line

Point (undefined term)

Indicates a location, has no size

Line (undefined term)

Extends infinitely, has no thickness, contains infinitely many…