Chapter 3 Notes

Front 1

Congruent Angle Postulate

Back 1

If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

Front 2

Slope of Parallel Line Postulate

Back 2

Parallel Lines have the same slope.

Front 3

Perpendicular Lines Postulate

Back 3

There slope is -1

Front 4

Plane and Transversal Postulate

Back 4

If two lines in a plane are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.

Front 5

Parallel Postulate

Back 5

If there is a line and a point not on the lines, then there exists exactly one line through the point that is parallel to the given line.

Front 6

Lines with positive slopes, do what?

Back 6

Rise

Front 7

Lines with negative slopes, do what?

Back 7

Fall

Front 8

Lines with a slope of zero?

Back 8

Horizontal Lines

Front 9

Lines with an undefined slope (Example 6/0)?

Back 9

Vertical Lines

Front 10

Alternative Interior Angles Theorem

Back 10

If two parallel lines are cut by a transversal, then each pair of alternative angles is CONGRUENT.

Front 11

CONSECUTIVE INTERIOR Angles Theorem

Back 11

If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is SUPPLEMENTARY.

Front 12

ALTERNATING EXTERIOR Angles Theorem

Back 12

If two parallel lines are cut by a tranversal, then each pair of alternate exterior angles is CONGRUENT,

Front 13

Perpendicular Transversal Theorem

Back 13

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

Front 14

Formula for SLOPE

Back 14

m = y2-y1/x2-x1

Front 15

Skew Lines

Back 15

Two lines that do NOT intersect and are NOT in the same plane.

Front 16

Parallel Lines

Back 16

Two lines in a place that never meet.

Front 17

Transversal Line

Back 17

a line that intersects two or more lines in a plane at diffferent points.

Front 18

Parallel Lines Theorem with Exterior Congruent Angles

Back 18

If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel.

Front 19

Parallel Lines Theorem with Consecutive Interior Angles (that are supplementary)

Back 19

If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is SUPPLEMENTARY, then the lines are parallel.

Front 20

Parallel Lines Theorem with Alternate Interior Angles

Back 20

If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel.

Front 21

Parallel Line Theorem with Perpendicular Lines

Back 21

In a plane if two lines are perpendicular to the same line, then they are parallel.

Front 22

Definition between a Point and a Line

Back 22

The distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point.

Front 23

Definition of the distance between parallel lines

Back 23

Definition of the distance between two parallel lines is the distance between one of the lines and any point on the other line.

Front 24

Postulate

Back 24

principles accepted as true without proof.

Front 25

Conjecture

Back 25

Educated Guess

Front 26

Counterexample

Back 26

An example used to show that a given general state is not always true.

Front 27

Conditional Statements

Back 27

These are "if" "then" statements.

Front 28

Converse

Back 28

Exchanging the hypothesis and conclusion of a conditional .
p q is q p

Front 29

Negation

Back 29

denial of a statement. P represent "not p" or negation of "p"

Front 30

Inverse of Conditional Statement

Back 30

given a conditional statement its inverse can be formed by negating both the hypothesis and conclusion. The inverse of a true statement is not necessarily true. The inverse of p q is "Not p not q"

Front 31

Inductive Reasoning

Back 31

when you see the same thing happeneing again and again (a pattern).

Front 32

Deductive Reasoning

Back 32

When you see the laws of logic and statement that are known to be true reach a conclsuion.

Front 33

Law of Detachment

Back 33

if p q is a true conditional and p is true than q is true.

Front 34

Law of Syllogism

Back 34

id p q and q r are true conditionals, then p r is also true.

Front 35

Postulates

Back 35

Principles accepted as true without proof.

Front 36

One Line Postulate

Back 36

Through any two points, there is exactly one line.

Front 37

One Plane Postulate

Back 37

Through any three points NOT on the sme line there is exactly one plane.

Front 38

Line Postulate

Back 38

A line contains at least two points.

Front 39

Place Postulate

Back 39

A plane contain at least three points not on the same line. For example Triangle.

Front 40

Line and Plane Postulate

Back 40

If two point line in a plane, then the entire line containing those two points line in that plane.

Front 41

Intersection of Two Planes Postulate

Back 41

If two plane intersect, then their INTERSECTION is a line.

Front 42

Congruence of Segments Postulate

Back 42

Congruence of segments is reflexive, symmetric and transitive.

Front 43

Reflexive Property

Back 43

a = a

Front 44

Symmetric Property

Back 44

if a = b then b = a

Front 45

Transitive Property

Back 45

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

Front 46

Addition and Subtraction Property

Back 46

a = b then a + c = b + c and
a - c = b - c

Front 47

Multiplication and Subtraction Property

Back 47

if a = b then a x c = b x c and
a/c = b/c

Front 48

Substitution Property

Back 48

if a = b then a may be replaced by b in any equation or expression.

Front 49

Reflexive Angles

Back 49

measure of angle 1 = measure of angle 1

Front 50

Symmetric Angles

Back 50

if measure of angle A = measure of anlge B then the measure of angle B = the measure of angle A

Front 51

Transitive Angles

Back 51

if the measure of angle 1 = the measure of agle 2 and the measure of angle 2 = the measure of angle 3, then the measure of angles 1 = measure of angles 3.

Front 52

Ruler Postulate

Back 52

Points on a line can be matched one to one with set of real numbers.

Front 53

Protractor postulate

Back 53

Rays from can be matched one for one with real numbers from 0 to 180 degrees.

Front 54

Angle Addition Postulate

Back 54

If B is in the interior of angle AOC then the measure of angle AOB + BOC = AOC

Front 55

Linear Pair Postulate

Back 55

If two anlges form a linear pair, then they are supplementary and their sum measures 180 degrees.

Front 56

Midpoint Theorem

Back 56

On a number line the corrinates of the midpoint of the segment with END points A and B is A + B /2.

Front 57

Angles

Back 57

Defined by two rays; extend indefinitely in two directions; share a common end point; seperate a plane into three parts(angle, interior, exterior); measured in degrees.

Front 58

Math Alert

Back 58

a linear pair ALWAYS forms supplementary angles BUT supplemeentary angles do NOT ALWAYS form a linear pair.