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# Chapter 3 Notes 2

## Terms

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Congruent Angle Postulate
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
Slope of Parallel Line Postulate
Parallel Lines have the same slope.
Perpendicular Lines Postulate
There slope is -1
Plane and Transversal Postulate
If two lines in a plane are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.
Parallel Postulate
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.
Lines with positive slopes, do what?
Rise
Lines with negative slopes, do what?
Fall
Lines with a slope of zero?
Horizontal Lines
Lines with an undefined slope (Example 6/0)?
Vertical Lines
Alternative Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternative angles is CONGRUENT.
CONSECUTIVE INTERIOR Angles Theorem
If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is SUPPLEMENTARY.
ALTERNATING EXTERIOR Angles Theorem
If two parallel lines are cut by a tranversal, then each pair of alternate exterior angles is CONGRUENT,
Perpendicular Transversal Theorem
In a plane, if a line is PERPENDICULAR to one of two parallel lines, then it is perpendicular to the other.
Formula for SLOPE
m = y2-y1/x2-x1
Skew Lines
Two lines that do NOT intersect and are NOT in the same plane.
Parallel Lines
Two lines in a place that never meet.
Transversal Line
a line that intersects two or more lines in a plane at diffferent points.
Parallel Lines Theorem with Exterior Congruent Angles
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.
Parallel Lines Theorem with Consecutive Interior Angles (that are supplementary)
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.
Parallel Lines Theorem with Alternate Interior Angles
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.
Parallel Line Theorem with Perpendicular Lines
In a plane if two lines are perpendicular to the same line, then they are parallel.
Definition between a Point and a Line
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.
Definition of the distance between parallel lines
Definition of the distance between two parallel lines is the distance between one of the lines and any point on the other line.
Postulate
principles accepted as true without proof.
Conjecture
Educated Guess
Counterexample
An example used to show that a given general state is not always true.
Conditional Statements
These are "if" "then" statements.
Converse
Exchanging the hypothesis and conclusion of a conditional .
p q is q p
Negation
denial of a statement. P represent "not p" or negation of "p"
Inverse of Conditional Statement
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"
Inductive Reasoning
when you see the same thing happeneing again and again (a pattern).
Deductive Reasoning
When you see the laws of logic and statement that are known to be true reach a conclsuion.
Law of Detachment
if p q is a true conditional and p is true than q is true.
Law of Syllogism
id p q and q r are true conditionals, then p r is also true.
Postulates
Principles accepted as true without proof.
One Line Postulate
Through any two points, there is exactly one line.
One Plane Postulate
Through any three points NOT on the sme line there is exactly one plane.
Line Postulate
A line contains at least two points.
Place Postulate
A plane contain at least three points not on the same line. For example Triangle.
Line and Plane Postulate
If two point line in a plane, then the entire line containing those two points line in that plane.
Intersection of Two Planes Postulate
If two plane intersect, then their INTERSECTION is a line.
Congruence of Segments Postulate
Congruence of segments is reflexive, symmetric and transitive.
Reflexive Property
a = a
Symmetric Property
if a = b then b = a
Transitive Property
if a = b and b = c, then a = c
Addition and Subtraction Property
a = b then a + c = b + c and
a - c = b - c
Multiplication and Subtraction Property
if a = b then a x c = b x c and
a/c = b/c
Substitution Property
if a = b then a may be replaced by b in any equation or expression.
Reflexive Angles
measure of angle 1 = measure of angle 1
Symmetric Angles
if measure of angle A = measure of anlge B then the measure of angle B = the measure of angle A
Transitive Angles
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.
Ruler Postulate
Points on a line can be matched one to one with set of real numbers.
Protractor postulate
Rays from can be matched one for one with real numbers from 0 to 180 degrees.