Ch. 1-3 Geometry Theorems

Front 1

Line Intersection Theorem

Back 1

Two different lines intersect in at most one point.

Front 2

Linear Pair Theorem

Back 2

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

Front 3

Vertical Angle Theorem

Back 3

If two angles are verticla angles, then they have equal measures.

Front 4

Paralell Lines and Slopes Theorem

Back 4

Two nonvertical lines are parallel if and only if they have the same slope.

Front 5

Two Perpendiculars Theorem

Back 5

In a plane, if l is perpendicular to n and m is perpendicular to n, the l is perpendicular to n.

Front 6

Perpendicular to Parallels Theorem

Back 6

In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.

Front 7

Perpendicular Lines and Slopes Theorem

Back 7

Two nonvertical lines are perpendicular if and only if the product of their slopes is -1.

Front 8

Unique Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 8

Throught any tow points, there is exactly one line.

Front 9

Number Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 9

Every line is a set of points that can be pit into a one-to-one correspindence with the real numbers, with any point on it cxorresponfing to 0 and any other point corresponding to 1.

Front 10

Dimension Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 10

(1) Given a line in a plane , there is at least on point in the plane thar s not on the line. (2) Given a plane in space. there is at least on point in space that is not in the plane.

Front 11

Flat Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 11

If two points lie in a plane, the line containing tem lies in the plane.

Front 12

Unique Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 12

Through two noncollinear points, there is exactly one point.

Front 13

Intersecting Planes Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 13

If two different planes have a point in common, then their intersection is a line.

Front 14

Uniqueness Property (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 14

On a line, there is a unigue distance between two points.

Front 15

Distance Formula (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 15

If the two points on a line have coordinates x and y, the distance between them is |x-y|.

Front 16

Additive Property (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 16

If B is on line segment AC, then AB+BC=AC.

Front 17

Triangle Inequality Postulate (Some Postylates for Arthmetic and Geometry)

Back 17

The sum of the lengths og any two sides of a truangle is greater than the length of the third side.

Front 18

Unique Measure Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry)

Back 18

Every angle has a unique measure from 0 degress to 180 degress.

Front 19

Unique Angle Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry)

Back 19

Given any ray ray VA and any real number r between 0 and 180, there is a unique angle BVA in each half-plane of line VA such that the measure of angle BVA=r.

Front 20

Unique Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 20

Throught any tow points, there is exactly one line.

Front 21

Number Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 21

Every line is a set of points that can be pit into a one-to-one correspindence with the real numbers, with any point on it cxorresponfing to 0 and any other point corresponding to 1.

Front 22

Dimension Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 22

(1) Given a line in a plane , there is at least on point in the plane thar s not on the line. (2) Given a plane in space. there is at least on point in space that is not in the plane.

Front 23

Flat Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 23

If two points lie in a plane, the line containing tem lies in the plane.

Front 24

Unique Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 24

Through two noncollinear points, there is exactly one point.

Front 25

Intersecting Planes Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 25

If two different planes have a point in common, then their intersection is a line.

Front 26

Uniqueness Property (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 26

On a line, there is a unigue distance between two points.

Front 27

Distance Formula (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 27

If the two points on a line have coordinates x and y, the distance between them is |x-y|.

Front 28

Additive Property (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 28

If B is on line segment AC, then AB+BC=AC.

Front 29

Triangle Inequality Postulate (Some Postylates for Arthmetic and Geometry)

Back 29

The sum of the lengths og any two sides of a truangle is greater than the length of the third side.

Front 30

Unique Measure Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry)

Back 30

Every angle has a unique measure from 0 degress to 180 degress.

Front 31

Unique Angle Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry)

Back 31

Given any ray ray VA and any real number r between 0 and 180, there is a unique angle BVA in each half-plane of line VA such that the measure of angle BVA=r.

Front 32

Unique Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 32

Throught any tow points, there is exactly one line.

Front 33

Number Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 33

Every line is a set of points that can be pit into a one-to-one correspindence with the real numbers, with any point on it cxorresponfing to 0 and any other point corresponding to 1.

Front 34

Dimension Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 34

(1) Given a line in a plane , there is at least on point in the plane thar s not on the line. (2) Given a plane in space. there is at least on point in space that is not in the plane.

Front 35

Flat Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 35

If two points lie in a plane, the line containing tem lies in the plane.

Front 36

Unique Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 36

Through two noncollinear points, there is exactly one point.

Front 37

Intersecting Planes Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates)

Back 37

If two different planes have a point in common, then their intersection is a line.

Front 38

Uniqueness Property (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 38

On a line, there is a unigue distance between two points.

Front 39

Distance Formula (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 39

If the two points on a line have coordinates x and y, the distance between them is |x-y|.

Front 40

Additive Property (Distance Postulate; Some Postylates for Arthmetic and Geometry)

Back 40

If B is on line segment AC, then AB+BC=AC.

Front 41

Triangle Inequality Postulate (Some Postylates for Arthmetic and Geometry)

Back 41

The sum of the lengths og any two sides of a truangle is greater than the length of the third side.

Front 42

Unique Measure Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry)

Back 42

Every angle has a unique measure from 0 degress to 180 degress.

Front 43

Unique Angle Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry)

Back 43

Given any ray ray VA and any real number r between 0 and 180, there is a unique angle BVA in each half-plane of line VA such that the measure of angle BVA=r.

Front 44

Relflexive Property Of equality

Back 44

a=a

Front 45

Symetric Property of Equality

Back 45

IFf a=b, the b=a.

Front 46

Transitive Property of Equality

Back 46

If a=b and b=c, then a=c.

Front 47

Addition Property of Equality

Back 47

If a=b, the a+c=b+c.

Front 48

Multiplucation Property of Equality

Back 48

If a=b, the ac=bc.

Front 49

Transitive Property of Inequality

Back 49

If a is less than b and b is less than c, the a is less than c.

Front 50

Addition Property of Inequality

Back 50

If a is less than b, than a+b is less than b+c

Front 51

Multiplucation Property of Inequality

Back 51

If a is less than b and c is less than 0, then ac is less than bc. If a is less than b and c is greater than 0, then ac is greater than bc.

Front 52

Equation to Inequality Property

Back 52

If a and b are positive numbers and a+b=c, then c is greater than a and c is greater than b.

Front 53

Substituation Property

Back 53

If a=b, then a may be substituted for b in any expression.

Front 54

Corresponding Angles Postulate

Back 54

(a) If two corresponding angles have the same measure, then the lines are parallel.
(b) If the lines are parallel, then corresponding angles have the same measure.