Glencoe Geometry

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Bell Work Hand-out Complete KWL and bell work
problems on back.
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PARALLEL LINES
Why are roller coasters built using parallel
lines? http//www.cedarpoint.com/public/park/rides
/coasters/gemini/index.cfm
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5-Minute Check 1
What is the slope of a line perpendicular to the
line above?

• A
• B
• C
• D

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5-Minute Check 3
What equation represents a line with slope 3
containing the point (0, 2.5) in slope-intercept
form?
A. y 3x 2.5 B. y 3x C. y 2.5 3x
D. y 3(x 2.5)

• A
• B
• C
• D

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5-Minute Check 6

• A
• B
• C
• D

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Then/Now
You used slopes to identify parallel and
perpendicular lines. (Lesson 33)

• Recognize angle pairs that occur with parallel
  lines.

• Prove that two lines are parallel.

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Concept
8
Concept
How might you apply this same idea to planes?
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Concept
What is your plan for remembering the meaning of
converse?
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Example 1
Identify Parallel Lines

• A. Given ?1 ? ?3, is it possible to prove that
  any of the lines shown are parallel? If so, state
  the postulate or theorem that justifies your
  answer.

?1 and ?3 are corresponding angles of lines a and
b.
Answer Since ?1 ? ?3, ab by the Converse of
the Corresponding Angles Postulate.
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Example 1
Identify Parallel Lines

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

?1 and ?4 are alternate interior angles of lines
a and c.
Answer Since ?1 is not congruent to ?4, line a
is not parallel to line c by the Converse of the
Alternate Interior Angles Theorem.
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Example 1
A. Given ?1 ? ?5, is it possible to prove that
any of the lines shown are parallel?
A. Yes l n B. Yes m n C. Yes l m D. It
is not possible to prove any of the lines
parallel.

• A
• B
• C
• D

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Example 1
B. Given m?4 105 and m?5 70, is it possible
to prove that any of the lines shown are parallel?
A. Yes l n B. Yes m n C. Yes l m D. It
is not possible to prove any of the lines
parallel.

• A
• B
• C
• D

If there were an angle numbered below angle 5,
what would the total of that angle and angle 5
be. Lets call it angle 7. Would angle 4 be equal
to angle 7?
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Example 2
Read the Test Item From the figure, you know
that m?WXP 11x 25 and m?ZYN 7x 35. You
are asked to find m?ZYN.
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Example 2
Solve the Test Item ?WXP and ?ZYN are alternate
exterior angles. For line PQ to be parallel to
MN, the alternate exterior angles must be
congruent. Som?WXP m?ZYN. Substitute the given
angle measures into this equation and solve for
x. Once you know the value of x, use substitution
to find m?ZYN.
11x 25 7x 35 Substitution 4x 25
35 Subtract 7x from each side. 4x 60 Add 25 to
each side. x 15 Divide each side by 4.
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Example 2
Now use the value of x to find m?ZYN.
m?ZYN 7x 35 Original equation
7(15) 35 x 15 140 Simplify.
Check Verify the angle measure by using the
value of x to find m?WXP.
m?WXP 11x 25
11(15) 25
140
Answer m?ZYN 140
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Example 2

• A
• B
• C
• D

If x is 9 and the two angles are equal, then what
is the measure of the angle RAB?
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Example 3
Prove Lines Parallel
CONSTRUCTION In the window shown, the diamond
grid pattern is constructed by hand. Is it
possible to ensure that the wood pieces that run
the same direction are parallel? If so, explain
how. If not, explain why not.
Answer Measure the corresponding angles formed
by two consecutive grid lines and the
intersecting grid line traveling in the opposite
direction. If these angles are congruent, then
the grid lines that run in the same direction are
parallel by the Converse of the Corresponding
Angles Postulate. If you were constructing this
grid by hand, what tool would you use to measure
your work?
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• Can you brainstorm some real world applications
  of parallel lines?
• Why must they be parallel?

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• Complete Practice Worksheet with your partner.

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End of the Lesson