Geometry Chapter 3 West

Front 1

Parallel lines

Back 1

two lines are this if they are coplanar and do not intersect

Front 2

Lines that do not intersect and are not coplanar are called

Back 2

skew lines

Front 3

Two planes that do not intersect are called

Back 3

Parallel planes

Front 4

transversal

Back 4

a line that intersects two or more coplanar lines at different points

Front 5

corresponding angles

Back 5

two angles are this if they occupy corresponding postions

Front 6

alternate exterior angles

Back 6

angles lying outside the two lines on opposite sides of the transversal

Front 7

two angles are __________ if they lie between the two lines on opposite sides of the transversal

Back 7

alternate interior angles

Front 8

Two angles are _____________ if they lie between the two lines on the same side of the transversal

Back 8

consecutive interior angles

Front 9

same side interior angles

Back 9

consecutive interior angles are sometimes called this

Front 10

________ ______ are coplaner and do not intersect

Back 10

Parallel Lines

Front 11

Skew Lines

Back 11

are noncoplaner and do not intersect.

Front 12

Parallel Postulate

Back 12

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

Front 13

If there is a line through the point perpendicular to the given line, then there is exactly one line through the point perpendicular to the given line

Back 13

Perpendicular Postulate

Front 14

If two lines are cut by a transversal so the corresponding angles are congruent then the lines are parallel

Back 14

Corresponding Angles Converse

Front 15

A transversal is a line that

Back 15

intersects two or more coplanar lines at different points

Front 16

Corresponding angles need to be ____________ in order for the lines to be parallel

Back 16

the same/congruent

Front 17

Consecutive interior angles are _____________ the lines are parallel

Back 17

supplementary

Front 18

Corresponding angles must be congruent for the lines to be ________

Back 18

parallel

Front 19

Alternate Interior Angles must be ___________ for the lines to be parallel

Back 19

congruent/ the same measure

Front 20

Vertical angles are

Back 20

congruent

Front 21

How do you determine if lines are parallel?

Back 21

1. If corresponding angles are congruent then the line are parallel
2. Alternate exterior angles are congruent
3. Alternate interior angles are congruent
4. consecutive exterior supplementary
5. Consecutive interior angles are supplentary

Front 22

How do you tell if two lines cut by a transversal are parallel?

Back 22

One way is to look for corresponding angles to be congruent.

Front 23

flow proof

Back 23

uses arrows to show the flow of the logical argument. Each reason in a flow proof is written below the statement it justifies

Front 24

Alternate Interior Angles Theorem

Back 24

If two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent.

Front 25

Consecutive Interior Angles Theorem

Back 25

If two parallel lines are cut by a transversal then the pairs of consectuvie interior angles are supplementary

Front 26

Alternate Exterior Angles Theorem

Back 26

If two parallel lines are cut by a transversal then the pairs of alternate exterior angles are congruent

Front 27

Perpendicular Transversal

Back 27

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other

Front 28

Corresponding Angles Postulate

Back 28

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Front 29

Corresponding Angles Converse

Back 29

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

Front 30

Alternate Interior Angles Converse

Back 30

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel

Front 31

Consecutive Interior Angles Converse

Back 31

If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel

Front 32

Alternate Exterior Angles Converse

Back 32

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel

Front 33

When you are given the angles you are working backwards and using

Back 33

the converse thereom

Front 34

Consecutive Interior angles are _____________

Back 34

supplementary

Front 35

Theorem 3.11 If two lines are parallel to the same line, then they are parallel to

Back 35

each other

Front 36

Theorem 3:11 If two lines are _____________ to the same line, then they are parallel to each other.

Back 36

parallel

Front 37

Theorem 3:12
In a plane, if two lines are perpendicular to the same line, then they are parallel to ________

Back 37

each other

Front 38

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

Back 38

plane

Front 39

Slopes of Lines
Lines with positive slope

Back 39

rise

Front 40

Lines with negative slope

Back 40

fall

Front 41

Vertical lines are

Back 41

undefined or "no slope"

Front 42

Horizontal slope are lines with a slope of

Back 42

zero

Front 43

slope equation is y=

Back 43

mx+b

Front 44

Postulate 17: Slopes of Parallel lines.
In a coordinate plane, two ___________ lines are parallel if and only if they have the same slope. Any two vertical lines are ____________

Back 44

nonvertical
parallel

Front 45

In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is

Back 45

-1

Front 46

Vertical and horizontal lines

Back 46

are perpendicular

Front 47

A line's slope that rises from left to right is

Back 47

Positive

Front 48

A vertical line's slope is

Back 48

undefined

Front 49

A horizontal line's slope is

Back 49

zero

Front 50

A line that falls from left to right has a ______ slope

Back 50

negative

Front 51

You can use the _______ of two lines to tell whether the lines are parallel

Back 51

slopes

Front 52

What information is contained in the equation of a line written in slope-intercept form?

Back 52

The slope of the line and y-intercept

Front 53

If you know two points on line p and two points on line q how could you tell if p is parallel to q?

Back 53

Find the slope of each line using the slope formula. If the slopes are equal, the lines are parallel

Front 54

Write an equation of the line whose slope is 2 and whose y-intercept is -1

Back 54

y=2x-1

Front 55

Line m is perpendicular to line n. If line m has a positive slope, what kind of slope does line n have?

Back 55

a negative slope

Front 56

Write an equation of line that has slope 4 and y intercept 10.

Back 56

y=4x+10

Front 57

Line M is perpendicular to line n. If line M has a positive slope, what kind of slope does line n have?

Back 57

a negative slope

Front 58

In a coordinate plane, two nonvertical lines are ________if and only if the ____of their slopes is -1. Vertical and horizontal lines are perpendicular

Back 58

perpendicular,
product

Front 59

The slope of one of two perpendicular lines is a/b. What is the slope of the other line?

Back 59

-b/a

Front 60

The ______ of two perpendicular lines are ____reciprocals of each other.

Back 60

slopes
negative

Front 61

Linear Pairs

Back 61

add up to 180 degrees

Front 62

Corresponding angles

Back 62

are equal

Front 63

1.identifying the angles
2.Knowing their relationship
3. looking at the lines and setting up their equation
4.being able to tell if the lines are parallel

Back 63

Key things to know when approaching problems in Chapter 3

Front 64

Consectutive Interior Converse

Back 64

If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel

Front 65

Vertical angles

Back 65

are congruent

Front 66

Corresponding Angles Converse

Back 66

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

Front 67

Alternate Interior Angles Converse

Back 67

If two lines are cut by a transversal so that alternate interior angles are congruen, then the lines are parallel

Front 68

Alternate Exterior Angles Converse

Back 68

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

Front 69

Concept to know:
Parallel lines have equal

Back 69

slopes

Front 70

Write an equation of the line uses:

Back 70

y= mx + b
slope intercept form

Front 71

Find the equation of a line whose y intercept is 3 and is parallel to y=x-8

Back 71

y=x + 3

Front 72

2 points are given
(-3,6) (0,3)
Find the equation of the line?
What do you need to do?

Back 72

1.Find the slope using the slope formula.
2. y=mx +b
Plug in slope for m
Plug in one of the points for y and x to get b
Put it all together in the slope intercept form y=mx + b

Front 73

The slopes of two _________ lines are negative reciprocals of each other.

Back 73

perpendicular

Front 74

In a coordinate plance, if two vertical lines are __________, then the product of their slopes is -1.

Back 74

perpendicular

Front 75

In a coordinate plane, if the product of the slopes of two lines is _______, then the lines are perpendicular.

Back 75

-1

Front 76

If you are trying to prove that two lines are _________ you use converse theorems.

Back 76

parallel

Front 77

If you are given the lines that are parallel and you are finding what angles are equal you uses

Back 77

theorem and postulates not theorem

Front 78

Corresponding angles are only equal if the two lines that form them are

Back 78

parallel

Front 79

If two angle measures are
2x-15 = x +30 they are

Back 79

congruent. We know that by the equal sign.

Front 80

Mrs West's Geometry test is

Back 80

Monday

Front 81

Complete the following to make a true statement;
In a plane, if two lines are ______ to the same line, then they are _______ to each other

Back 81

perpendicular, Parallel
OR
parallel, parallel