# Chapter 3: Parallel and Perpendicular Lines - PowerPoint PPT Presentation

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## Chapter 3: Parallel and Perpendicular Lines

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### Chapter 3: Parallel and Perpendicular Lines Lesson 1: Parallel Lines and Transversals – PowerPoint PPT presentation

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Title: Chapter 3: Parallel and Perpendicular Lines

1
Chapter 3 Parallel and Perpendicular Lines
• Lesson 1 Parallel Lines and Transversals

2
Definitions
• Parallel lines ( )- coplanar lines that do not
intersect (arrows on lines indicate which sets
are parallel to each other)
• Parallel planes- two or more planes that do not
intersect
• Skew lines- lines that do not intersect but are
not parallel (are not coplanar)
• Transversal- a line that intersects two or more
lines in a plane at different points

3
Pairs of angles formed by parallel lines and a
transversal (see graphic organizer for examples)
• Exterior angles outside the two parallel lines
• Interior angles between the two parallel lines
• Consecutive Interior angles between the two
parallel lines, on the same side of the
transversal
• Consecutive Exterior angles outside the two
parallel lines, on the same side of the
transversal
• Alternate Exterior angles outside the two
parallel lines, on different sides of the
transversal
• Alternate Interior angles between the two
parallel lines, on different sides of the
transversal
• Corresponding angles one outside the parallel
lines, one inside the parallel lines and both on
the same side of the transversal

4
C. Name a plane parallel to plane ABG.
5
Classify the relationship between each set of
angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles
A. ?2 and ?6
B. ?1 and ?7
C. ?3 and ?8
D. ?3 and ?5
6
A. Identify the sets of lines to which line a is
a transversal.
B. Identify the sets of lines to which line b is
a transversal.
C. Identify the sets of lines to which line c is
a transversal.
7
Chapter 3 Parallel and Perpendicular Lines
• Lesson 2 Angles and Parallel Lines

8
If two parallel lines are cut by a transversal,
then (see graphic organizer)
• the alternate interior angles are congruent
• the consecutive interior angles are supplementary
• the alternate exterior angles are congruent
• the corresponding angles are congruent
• In a plane, if a line is perpendicular to one of
the two parallel lines, then it is also
perpendicular to the other line.

9
A. In the figure, m?11 51. Find m?15. Tell
which postulates (or theorems) you used.
B. In the figure, m?11 51. Find m?16. Tell
which postulates (or theorems) you used.
10
A. In the figure, a b and m?20 142. Find
m?22.
B. In the figure, a b and m?20 142. Find
m?23.
11
A. ALGEBRA If m?5 2x 10, and m?7 x 15,
find x.
B. ALGEBRA If m?4 4(y 25), and m?8 4y,
find y.
12
1. ALGEBRA If m?1 9x 6, m?2 2(5x 3), and
m?3 5y 14, find x.

B. ALGEBRA If m?1 9x 6, m?2 2(5x 3), and
m?3 5y 14, find y.
13
Chapter 3 Parallel and Perpendicular Lines
• Lesson 5 Proving Lines Parallel

14
If (see graphic organizer)
• Corresponding angles are congruent,
• Alternate exterior angles are congruent,
• Consecutive interior angles are supplementary,
• Alternate interior angles are congruent,
• Two lines are both perpendicular to the
transversal,
• Then the lines are parallel.
• If given a line and a point not on the line,
there is exactly one line through that point that
is parallel to the given line

15
If so, state the postulate or theorem that
A. Given ?1 ? ?3, is it possible to prove that
any of the lines shown are parallel?
• B. Given m?1 103 and m?4 100, is it
possible to prove that any of the lines shown are
parallel?.

16
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17
A. Given ?9 ? ?13, which segments are parallel?
B. Given ?2 ? ?5, which segments are parallel?
18
Chapter 3 Parallel and Perpendicular Lines
• Lesson 3 Slopes of Lines

19
Slope
• The ratio of the vertical rise over the
horizontal run
• Can be used to describe a rate of change
• Two non-vertical lines have the same slope if and
only if they are parallel
• Two non-vertical lines are perpendicular if and
only if the product of their slopes is -1

20
Foldable
• Step 1 fold the paper into 3 columns/sections
• Step 2 fold the top edge down about ½ inch to
form a place for titles. Unfold the paper and
turn it vertically.
• Step 3 title the top row Slope, the middle row
Slope-intercept form and the bottom row
Point-slope form

21
Slope
• Rise 0 zero slope (horizontal line)
• Run 0 undefined (vertical line)
• Parallel same slope
• Perpendicular one slope is the reciprocal and
opposite sign of the other
• Ex find the slope of a line containing (4, 6)
and (-2, 8)

22
Find the slope of the line.
23
Find the slope of the line.
24
Find the slope of the line.
25
Find the slope of the line.
26
• Determine whether FG and HJ are parallel,
perpendicular, or neither for F(1, 3), G(2,
1), H(5, 0), and J(6, 3).
• (DO NOT GRAPH TO FIGURE THIS OUT!!)

27
• Determine whether AB and CD are parallel,
perpendicular, or neither for A(2, 1),
• B(4, 5), C(6, 1), and D(9, 2)

28
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29
Chapter 3 Parallel and Perpendicular Lines
• Lesson 4 Equations of Lines

30
Slope-intercept form y mx b
Slope and y-intercept Two ordered-pairs (one is y-intercept) Two ordered-pairs (neither is y-intercept)
m -4 y-intercept 7 (4, 1) (0, -2) (3, 3) (2, 0)
This should be your middle row on the foldable
31
Point-slope form
Slope and one ordered-pair Two ordered-pairs
m (7, 2) (8, -2) (-3, -1)
This should be your bottom row on the foldable
32
• Write an equation in slope-intercept form of the
line with slope of 6 and y-intercept of 3.

33
• Write the equation in slope-intercept form and
then

34
• Write an equation in slope-intercept form for a
line containing (4, 9) and (2, 0).

35
• Write an equation in point-slope form for a line
containing (3, 7) and
• (1, 3).

36
On the back
37
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38
Chapter 3 Parallel and Perpendicular Lines
• Lesson 6 Distance Between Parallel Lines

39
Perpendicular Lines and Distance
• The shortest distance between a line and a point
not on the line is the length of the
perpendicular line connecting them
• Equidistant the same distance- parallel lines
are equidistant because they never get any closer
or farther apart
• The distance between two parallel lines is the
distance between one line and any point on the
other line
• In a plane, if two lines are equidistant from a
third line, then the two lines are parallel to
each other

40
Steps to find the distance between parallel lines
1. Change the first equation so that the slope is
now perpendicular to the given slope. (do not
change anything else)
2. Set the new equation equal to the second given
equation
3. Solve for x.
4. Plug in for x in the new equation (the one with
the perpendicular slope) and solve for y.
5. Find the distance between the ordered pair
created with x and y and the y-intercept from the
changed equation (the one with perpendicular
slope).

41
• Find the distance between each pair of lines
• y 2x 1
• y 2x - 4

42
• Find the distance between the two parallel lines
• y x 2
• y x -