#### Study sets matching "geometry theorems postulates"

#### Study sets matching "geometry theorems postulates"

Segment Addition Postulate

Angle Addition Postulate

Linear Pain Postulate

Vertical Angles Theorem

If three points A, B and C are collinear and B is between A a…

If point B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m…

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

Vertical angles are congruent.

Segment Addition Postulate

If three points A, B and C are collinear and B is between A a…

Angle Addition Postulate

If point B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m…

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 in a one-to-one correspond…

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

Given a point, X, on line PR, consider ray XP and ray XR as w…

If point D is in the interior of angle ABC, then the m of ang…

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

Axiom 1

Axiom 2

Axiom 3

Axiom 4

things that are equal to the same thing and are equal to each…

if equals are added to equals, the sums are equal

if equals are subtracted from equals, the differences are equal

things that are alike or coincide with one another are equal…

Axiom 1

things that are equal to the same thing and are equal to each…

Axiom 2

if equals are added to equals, the sums are equal

Postulate 1: Ruler Postulate

Postulate 2: Segment Addition Postulate

Postulate 3: The Protractor Postulate…

Postulate 4: The Angle Addition Postul…

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

Given a point X on line PR, consider rays XP and XR, as well…

If point D is in the interior of angle ABC, then the measure…

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

Diagonals of a Rectangle Theorem

Diagonals of a Rhombus Theorem

Bisecting Diagonals of a Rhombus Theorem

Midpoint of a Hypotenuse Theorem

The diagonals of a retangle are congruent.

The diagonals of a rhombus are perpendicular.

Each diagonal of a rhombus bisects the two angles of the rhom…

The midpoint of the hypotenuse of a right triangle is equidis…

Diagonals of a Rectangle Theorem

The diagonals of a retangle are congruent.

Diagonals of a Rhombus Theorem

The diagonals of a rhombus are perpendicular.

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.

Point-Line Postulate

Isosceles Triangle Theorem

Isoceles Triangle Converse

Linear Pair Postulate

-Between two points it is possible to construct exactly one l…

If two sides of a triangle are of a triangle are congruent, t…

If two angles of a triangle are congruent, then the sides opp…

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

Point-Line Postulate

-Between two points it is possible to construct exactly one l…

Isosceles Triangle Theorem

If two sides of a triangle are of a triangle are congruent, t…

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, they intersect at exactly on…

If two distinct planes intersect, they intersect at exactly o…

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

If two distinct lines intersect, they intersect at exactly on…

supplement theorem

SAP

point-line postulate

point-plane theorem

supplements of congruent angles (or the same angle) are congr…

if AB = CD, then AB + BC = BC + CD

given any two points, there exists exactly one line containin…

given any three non-collinear points there exists exactly one…

supplement theorem

supplements of congruent angles (or the same angle) are congr…

SAP

if AB = CD, then AB + BC = BC + CD

Segment Addition Postulate:

The Protractor Postulate:

Congruent Complements Theorem

Right Angles Theorem:

If 3 points, A, B, and C are collinear and B is between A and…

The protractor postulate states that the measurement of an an…

If angle A and angle B are complements of the same angle, the…

All right angles are congruent

Segment Addition Postulate:

If 3 points, A, B, and C are collinear and B is between A and…

The Protractor Postulate:

The protractor postulate states that the measurement of an an…

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 ray OB and a point A on one side of ray OB. The rays…

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. If AB + BC = AC,…

Complementary Angles

Supplementary angles

theorem

Vertical angles

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

4 angles formed by intersecting lines and facing in four diff…

Complementary Angles

Two angles whose measures equal 90 degrees

Supplementary angles

two angles whose measures equal 180 degrees

Segment Addition postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Same-Side Interior Angles Theorem

AB+BC=AC

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…

Segment Addition postulate

AB+BC=AC

Alternate Interior Angles Theorem

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

reflexive property

symmetric property

transitive property

postulate

a quantity is equal to itself

an equation may be expressed in either order

if quantities are equal to the same quantity, they are equal…

a statement whose truth is accepted without proof

reflexive property

a quantity is equal to itself

symmetric property

an equation may be expressed in either order

If B is between A & C then AB + BC =AC

If two angles have the same measuremen…

If the angles are congruent two angles…

If a point, X, is in the interior of <…

segment addition postulate

definition of congruent angles

definition of congruent angles

angle addition postulate

If B is between A & C then AB + BC =AC

segment addition postulate

If two angles have the same measuremen…

definition of congruent angles

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…

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

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 is 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

What is a theorem?

What is theorem 1?

What is theorem 2?

What is theorem 3?

A statment that can be proven

If two lines intersect, then they intersect in exactly one po…

Through a line and a point not in the line there is exactly o…

If two lines intersect, then exactly one plane contains the l…

What is a theorem?

A statment that can be proven

What is theorem 1?

If two lines intersect, then they intersect in exactly one po…

Given two points...

Ruler Postulate

On a ray, there is exactly one point t…

If M is the midpoint of segment AB,

there is a unique distance between them.

There is a one to one correspondence between the two points o…

a given distance from the endpoint of the ray.

then 2AM = AB and AM = 1/2 AB.

Given two points...

there is a unique distance between them.

Ruler Postulate

There is a one to one correspondence between the two points o…

Definition of Midpoint

Definition of Bisector

Definition of Angle Bisector

Definition of Perpendicular

The point halfway between two given points.

A line segment, line, or plane that divides a geometric figur…

A line or ray that divides an angle in half.

Two lines bisect and form a 90 degree angle.

Definition of Midpoint

The point halfway between two given points.

Definition of Bisector

A line segment, line, or plane that divides a geometric figur…

segment addition postulate

angle addition posulate

postulate 5

postulate 6

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

If D is in the interior of ∠ABC, then the measure of ∠ABC is…

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 posulate

If D is in the interior of ∠ABC, then the measure of ∠ABC is…

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…

addition property of equality

subtraction property of equality

multiplication property of equality

division property of equality

if a=b then a+c= b+c... you can add something to both sides of a…

if a=b then a-c= b-c... you can subtract something from both sid…

if a=b then a x c = b x c... you can multiply both sides of an e…

if a=b then a/c= b/c... you can divide both side of an equation…

addition property of equality

if a=b then a+c= b+c... you can add something to both sides of a…

subtraction property of equality

if a=b then a-c= b-c... you can subtract something from both sid…

Segment Addition Postulate

Angle Addition Postulate

Two-Point Postulate

Line-Point Postulate

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

If P is in the interior of ∠RST, then the measure of ∠RST is…

Through any two points, there is exactly one line.

A line contains at least two points.

Segment Addition Postulate

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

Angle Addition Postulate

If P is in the interior of ∠RST, then the measure of ∠RST is…

Parallel lines

Skew Lines

Parallel Planes

Consecutive Interior Angles

Coplanar lines that do not intersect

Lines that do not intersect and are not coplanar

Planes that do not intersect

interior angles that lie on the same side of a transversal

Parallel lines

Coplanar lines that do not intersect

Skew Lines

Lines that do not intersect and are not coplanar

Surface Area

Lateral Area right prism

Volume of right prism

Lateral Area of regular pyramid

lateral area + 2B

Ph (Perimeter x height)

Bh (total area of Base x height)

1/2 P ℓ (ℓ = slant height)

Surface Area

lateral area + 2B

Lateral Area right prism

Ph (Perimeter x height)

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

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

What is the difference between a postu…

Ruler Postulate

Segment Addition Postulate

Linear Pair Theorem

A postulate is a rule accepted without proof. A theorem is a…

points on a line can be matched 1 to 1 with real numbers

B is between A and C if AB + BC = AC

if angle A and angle B form a linear pair, the measure of ang…

What is the difference between a postu…

A postulate is a rule accepted without proof. A theorem is a…

Ruler Postulate

points on a line can be matched 1 to 1 with real numbers

Addition property

subtraction property

multiplication property

division property

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

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

if a=b, then a

**c=b**cif a=b and c does not equal 0, then a/c = b/c

Addition property

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

subtraction property

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

segment addition postulate (SAP)

angle addition postulate (AAP)

addition property of equality

subtraction property of equality

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

Angles can be added together if they are adjacent

Adding a value to each side of an equation... if a=b, then a+c=b+c

subtracting a value from each side of an equation ... if a=b the…

segment addition postulate (SAP)

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

angle addition postulate (AAP)

Angles can be added together if they are adjacent

The Ruler Postulate

Segment Addition postulate

Protractor Postulate

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 (implies, A, B, an…

On AB in a given plane, choose any point O between A and B. C…

If point B lies in the interior of <AOC, then... m<AOB = m< BOC…

The Ruler Postulate

The points on a line can be paired with real numbers in such…

Segment Addition postulate

If B is between A and C, then AB + BC = AC (implies, A, B, an…

Theorem 3-7

Theorem 3-8

Perpendicular Transversal Theorem

Parallel Postulate

If two lines are parallel to the same line, then they are par…

In a plane, if two lines are perpendicular to the same line,…

In a plane, if a line is perpendicular to one of two parallel…

Through a point not on a line, there is one and only one line…

Theorem 3-7

If two lines are parallel to the same line, then they are par…

Theorem 3-8

In a plane, if two lines are perpendicular to the same line,…

Ruler postulate

Segment addition postulate

Protractor postulate

Angle addition postulate

the distance between A and B is the Absolute value of the dif…

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

The measure of angle ABC is equal to the absolute value of th…

If D is in the interior if angle ABC...... m<ABC=m<ABD+m<DBC

Ruler postulate

the distance between A and B is the Absolute value of the dif…

Segment addition postulate

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

Theorem 10.1

Theorem 10.2

Postulate 23

Theorem 10.3

In a plane, a line is tangent to a circle if and only the lin…

Tangent segments from a common external point are congruent

The measure of an arc formed by two adjacent arcs is the sum…

In the same circle, or in congruent circles, two minor arcs a…

Theorem 10.1

In a plane, a line is tangent to a circle if and only the lin…

Theorem 10.2

Tangent segments from a common external point are congruent

Addition property of inequality (≠)

multiplication and division property o…

transitive property of inequality (≠)

Property of inequality (≠)

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

If a > b and c > 0, then ac > bc and a/c > b/c;... If a > b and…

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

If a = b + c and c > 0, then a > b and a> c

Addition property of inequality (≠)

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

multiplication and division property o…

If a > b and c > 0, then ac > bc and a/c > b/c;... If a > b and…

Corresponding Angles Converse Postulate

Alternate Interior Angles Converse The…

Alternate Exterior Angles Converse The…

Consecutive Interior Angles Converse T…

if two lines are cut by a transversal so that corresponding a…

if two lines are cut by a transversal so that alternate inter…

if two lines are cut by a transversal so that alternate exter…

if two lines are cut by a transversal so that the consecutive…

Corresponding Angles Converse Postulate

if two lines are cut by a transversal so that corresponding a…

Alternate Interior Angles Converse The…

if two lines are cut by a transversal so that alternate inter…

segment addition postulate

angle addition postulate

linear pair postualte

reflexive property

if 3 points a, b, and c are colinear and b is between a and c…

if point b is interior of <aoc; then m<aob + m<boc = m<aoc

if two angles form a linear pair; they must be supplementary

a = a

segment addition postulate

if 3 points a, b, and c are colinear and b is between a and c…

angle addition postulate

if point b is interior of <aoc; then m<aob + m<boc = m<aoc

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Theorem

Right Angle Congruence Theorem (or Rig…

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

If O is in the interior of <ABC, then m<ABO + m<OBC = m<ABC

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

All right angles are congruent.

Segment Addition Postulate

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

Angle Addition Postulate

If O is in the interior of <ABC, then m<ABO + m<OBC = m<ABC

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Consecutive Interior Angles Theorem

Alternate Exterior Angles Theorem

When 2 lines are cut by a transversal, if the lines are paral…

When 2 lines are but by a transversal, if the lines are paral…

When 2 lines are cut by a transversal, if the lines are paral…

When 2 lines are cut by a transversal, if the lines are paral…

Corresponding Angles Postulate

When 2 lines are cut by a transversal, if the lines are paral…

Alternate Interior Angles Theorem

When 2 lines are but by a transversal, if the lines are paral…

Polygon Angle Sum Theorem

Polygon Exterior Angle Sum Theorem

Theorem 6.2.1 (Opp. sides parallelogra…

Theorem 6.2.2 (Opp. angles parallelogr…

The sum of the interior angle measures of a convex polygon wi…

The sum of the exterior angle measures, one angle at each ver…

If a quadrilateral is a parallelogram, then its opposite side…

If a quadrilateral is a parallelogram, then its opposite angl…

Polygon Angle Sum Theorem

The sum of the interior angle measures of a convex polygon wi…

Polygon Exterior Angle Sum Theorem

The sum of the exterior angle measures, one angle at each ver…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Ruler Postulate: The points on a line can be paired with the…

Segment Addition Postulate: If B is between A and C, then AB…

Protractor Postulate: On line AB in a given plane, choose any…

Angle Addition Postulate: If point B lies in the interior of…

Postulate 1

Ruler Postulate: The points on a line can be paired with the…

Postulate 2

Segment Addition Postulate: If B is between A and C, then AB…