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Transcript
```3-3 Proving Lines Parallel
What you need…….
PHONES AWAY
New Warm-Up Sheet
Pencil/Pen
Notebook
Holt McDougal Geometry
3-3 Proving Lines Parallel
Warm-Up 10/24
1. Go grab your assigned chrome book
2. Go to my website
3. Scroll to bottom and click link for Student
Feedback Survey
4. Take your time to think and complete this
survey. BE HONEST. THIS IS NOT FOR A
5. When finished, go to Khan Academy and
complete Line and Angles module and
One-step inequalities module
Holt McDougal Geometry
3-3 Proving Lines Parallel
What you need……. TURN PACKET IN!
PHONES AWAY
New Warm-Up Sheet
Pencil/Pen
Notebook
Holt McDougal Geometry
3-3 Proving Lines Parallel
Warm-Up 10/25
If l ll m, find the value of each missing
variable(s).
Holt McDougal Geometry
3-3 Proving Lines Parallel
Objective
I can use what I know about angles
formed by a transversal to prove two
lines are parallel.
PROVE IT?!
Holt McDougal Geometry
3-3 Proving Lines Parallel
What is the difference between these two
statements?
Hypothesis: "If the space shuttle was
launched, then a cloud of smoke was
seen."
Converse: "If a cloud of smoke was
seen, then the space shuttle was launched
The Converse of a theorem is found by
switching the hypothesis and conclusion.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Holt McDougal Geometry
3-3 Proving Lines Parallel
Check It Out! Example 1a
Use the Converse of the Corresponding Angles
Postulate and the given information to show
that ℓ || m.
m 1 = m  3
1  3
ℓ || m
Holt McDougal Geometry
1 and 3 are
corresponding angles.
Conv. of Corr. s Post.
3-3 Proving Lines Parallel
Holt McDougal Geometry
3-3 Proving Lines Parallel
Holt McDougal Geometry
3-3 Proving Lines Parallel
What you need…….TURN PACKET IN THAT WAS
DUE YESTERDAY
PHONES AWAY
Warm-Up Sheet
Pencil/Pen
Proving Lines Parallel Sheet from yesterday
Holt McDougal Geometry
3-3 Proving Lines Parallel
Warm-Up 10/26
Use the Converse of the Corresponding Angles
Postulate and the given information to show
that ℓ || m.
Given:4  8
4  8
ℓ || m
Holt McDougal Geometry
4 and 8 are corresponding angles.
Conv. of Corr. s Post.
3-3 Proving Lines Parallel
Example 3: Proving Lines Parallel
Given: p || r , 1  3
Prove: ℓ || m
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 3 Continued
Statements
Reasons
1. p || r
1. Given
2. 1  3
2. Given
3. 3  2
3. Alt. Ext. ’s Thm.
4. 1  2
4. Trans. Prop. of 
5. ℓ ||m
5. Conv. of Corr. s Post.
Holt McDougal Geometry
3-3 Proving Lines Parallel
You have 6 minutes to work on #3 and #4
from our worksheet yesterday. #4 is
challenging but I BELIEVE IN YOU!
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 1B: Using the Converse of the
Corresponding Angles Postulate
Use the Converse of the Corresponding Angles
Postulate and the given information to show
that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
m3 = 4(30) – 80 = 40
m7 = 3(30) – 50 = 40
Substitute 30 for x.
Substitute 30 for x.
m3 = m7
3  7
ℓ || m
Trans. Prop. of Equality
Def. of  s.
Conv. of Corr. s Post.
Holt McDougal Geometry
3-3 Proving Lines Parallel
For the next part of class, you need a white
board, marker and eraser. EVERYONE
NEEDS ONE OF EACH.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 2B Continued
Use the given information and the theorems you
have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5
m2 + m3 = 58° + 122°
= 180°
r || s
Holt McDougal Geometry
2 and 3 are same-side
interior angles.
Conv. of Same-Side Int. s Thm.
3-3 Proving Lines Parallel
Check It Out! Example 2b
Refer to the diagram. Use the given information
and the theorems you have learned to show
that r || s.
m3 = 2x, m7 = (x + 50),
x = 50
m3 = 2x
= 2(50) = 100°
Substitute 50 for x.
m7 = x + 50
= 50 + 50 = 100°
Substitute 5 for x.
m3 = 100 and m7 = 100
3  7
r||s Conv. of the Alt. Int. s Thm.
Holt McDougal Geometry
3-3 Proving Lines Parallel
What you need…….TURN PACKET IN
AND TURN IN PROVING LINES PARALLEL WS!!
PHONES AWAY
Warm-Up Sheet
Pencil/Pen
Notes
Holt McDougal Geometry
3-3 Proving Lines Parallel
Warm-Up 10/27
Refer to the diagram to
the right. Use the given
information and the
theorems you have
learned to show that
n ll p
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 4: Carpentry Application
A carpenter is creating a woodwork pattern
and wants two long pieces to be parallel.
m1= (8x + 20)° and m2 = (2x + 10)°. If
x = 15, show that pieces A and B are
parallel.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Check It Out! Example 4
What if…? Suppose the
corresponding angles on
the opposite side of the
boat measure (4y – 2)°
and (3y + 6)°, where
y = 8. Show that the oars
are parallel.
4y – 2 = 4(8) – 2 = 30°
3y + 6 = 3(8) + 6 = 30°
The angles are congruent, so the oars are || by the
Conv. of the Corr. s Post.
Holt McDougal Geometry
```
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