Chapter 1 Set, Statement And Reasoning

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Statement

Back 1

Is a set of words and symbols that collectively make a claim that can be classified as true or false . It can be simple or compound.conjunction

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conjunction

Back 2

Is two simple statements joined by the word "and". It is only true when both statements are true.

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Disjunction

Back 3

Is to simple statements showing by the word or.is false only win both statements are false.

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A statement of the form " If...., then..."

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Is an implication, or compound statement.

Alternate versions of a conditional

statement are "if P, then Q"

and if P Q where P is the

hypothesis and Q is the conclusion.

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Negation

Back 5

Of a given statement makes a claim opposite that of the original statement. Given a statement P, the Negation is denoted ~P ; read as "not P"

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Intuition

Back 6

Is the type of reasoning in which inspiration or past experience leads to a statement of theory

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Induction

Back 7

Is the type of reasoning in which an organized effort is made to test a theory. A specific observations and experiments to make the general conclusion.

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Deduction

Back 8

Is the type of reasoning in which the knowledge and acceptance of a selected assumptions guarantee the truth of a particular conclusion.

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Law of detachment

Back 9

Is an excepted format of a valid argument in which we use fax, known as premises of an argument, and on the basis of the premises, a particular conclusion must follow.

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Point

Back 10

A location in space, denoted by a dot and labeled with a capital letter.

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Line

Back 11

Is an infinite collection of points.

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Plane

Back 12

Is a two dimensional object that extends infinitely into both directions, yet has no thickness.

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Line segment

Back 13

Is part of a line, consisting of two distinct points on the line and all points between.

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Collinear

Back 14

Point are collinear if they lie on the same line. We use the following notation to show points between: P-Q-R

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Midpoint

Back 15

if point X divides line segment into two segments of equal measures point X is called the midpoint.

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Parallel

Back 16

Lines are coplanar Lines that are everywhere equidistant.

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Bisected

Back 17

Is divided into two parts of equal measures.

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Angle

Back 18

Is the union of two rays that share a common endpoint, called the vertex.

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Intersect

Back 19

When two lines have a point in common.

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Perpendicular

Back 20

When two lines intersect and form congruent adjacent angles.

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Line segments

Back 21

Is the part of a line that consists of two points, known as in points, and all points between them.

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Ray

Back 22

The part of a line that begins at a point and extends infinitely far in One Direction.

AB, denoted by a AB, is the union of AB and all points X on AB such that he is between A and X

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Congruent

Back 23

Geometric figures that can be made to coincide (fit perfectly fit perfectly one on top of another)

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Congruent line segments

Back 24

Two lines find segments that have The same length.

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Congruent segments

Back 25

Are two segments that have the same length.

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Parallel lines

Back 26

Are lines that night in the same plane but do not intersect.

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Postulate

Back 27

A statement that is assumed to be true.

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Postulate 1 Ch. 3

Back 28

Through two distinct points, there is exactly one line.

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Postulate 2 ( ruler postulate )

Ch. 3

Back 29

The measure of any line segment and a unique positive number.

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Distance

Back 30

Between two points A and B is the length of a line segment AB that joins the two points.

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Postulate 3 ( segment addition postulate )

Ch.3

Back 31

If X is a point of AB and A- X – B, then AX +XB=AB

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Postulate 4

Back 32

If two lines intersect, they intersect at a point.

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Postulate 5

Back 33

through three non-collinear points, there is exactly one plane.

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Non-coplanar points

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Four or more points that do not lie in the same plane.

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Noncollinear points

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Three or more points that do not lie in the same plane.

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Postulate 6

Back 36

If two distinct planes intersect, then there intersection is a line.

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Postulate 7

Back 37

Give into distinct points in a plane, The line containing these points also lies in the plane.

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Theorem 1.3.1

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The midpoint of a line segment is unique

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Congruent angles

Back 39

two angles with the same measure.

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Postulate 8 ( protractor postulate )

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The measure of an angle is a unique positive number

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Adjacent angle

Back 41

Two angles that share a common side and a common vertex but no common interior points.

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Bisector

Back 42

The bisector of an angle is the read that separates the given angle into two congruent angles. Similar to the midpoint of a line segment, the bisector of an angle is unique.

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Complementary

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Two angles are complementary if the sum of the measures is 90°

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Supplementary

Back 44

Two angles are supplementary if the sum of their measure is 180°

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Vertical angles

Back 45

Vertical anglesif two straight lines intersect, the Paris of non-adjacent angles formed are called vertical angles. In general vertical angles are congruent.

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Addition property of equality

Back 46

A =B then A +C = B+ C

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Subtraction property of equality

Back 47

A =B then A - C = B - C

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Multiplication property of equality

Back 48

A = B then AC = BC

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Division property of equality

Back 49

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

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Reflexive property

Back 50

A = A

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Symmetry property

Back 51

If a = B, then B = A

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Distributive property

Back 52

A(b+c)= a•b+ a•c

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Substitution property

Back 53

If a Inglesby, then a replaces be in any equation

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Transitive property

Back 54

If A = B and B = C, then A = C

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Union

Back 55

The joining together of two sets, such as Geometric figures.

The union of A with is the set of elements in A or B.

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Intersection

Back 56

The points that to geometric figure share .

The intersection of A with B is the set of elements in A and B.

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Subset

Back 57

A set of which all elements are contained in another set.

C is the subset of the every element of C is an element of D.

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Perpendicular lines

Back 58

Are two lines that meet to form congruent adjacent angles

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Theorem 1.6.1

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If two lines are perpendicular, then they meet to form a right angle

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Theorem 1.6.2

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If two lines intersect, then the local angles formed are congruent.

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Theorem 1.6.3

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In a plane, there is exactly one line perpendicular to the given line at any point on the line

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Theorem 1.6.4

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The perpendicular bisector of a line segment is unique

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Essential parts of the formal proof of my theorem

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1. Statement: States the theorem to be proved
2. Drawing: represents the hypothesis of the theorem
3. Given : describes the drying according to the information found in the hypothesis of the theorem
4. Prove: Describes the drawing according to the claim made and the conclusion of the theorem
5. Proof: or is a list of claims statements and justification reasons beginning with the given and the end with the proof; there must be a logical flow in this proof

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Theorem 1.7.1

Back 64

If two lines meet to form a right angle, then these lines are perpendicular

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Theorem. 1.7.2

Back 65

If two angles are complementary to the same angle or two congruent angles, then these angles are congruent

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Theorem 1.7.3

Back 66

If two angles are supplementary to the same angle or two congruent angles, in these angles are congruent

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Theorem 1.7.4

Back 67

Any two right angles are congruent

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Theorem. 1.7.5

Back 68

If the exterior sides of two adjacent acute angles form perpendicular raise, then these angles are complementary

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Theorem 1.7.6

Back 69

If the exterior side of two adjacent angles form a straight line, then these angles are supplementary

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Theorem 1.7.7

Back 70

If two line segments are congruent then there midpoint separate the segments into four congruent segments

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Theorem 1.7.8

Back 71

If two angles are congruent, then there bisector separate these angles and four congruent angles