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Proving Lines Parallel 3-4C

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p. 207 You found slopes of lines and used them to identify parallel and perpendicular lines. Recognize angle pairs that occur with parallel lines. – PowerPoint PPT presentation

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Title: Proving Lines Parallel 3-4C


1
Proving Lines Parallel 3-4C
  • p. 207

You found slopes of lines and used them to
identify parallel and perpendicular lines.
  • Recognize angle pairs that occur with parallel
    lines.
  • Prove that two lines are parallel.

2
Are these lines parallel?
  • Is there information in this figure to assume
    that the lines are parallel?

What information from the last section can we
use to show that these lines are parallel. What
do we need to add first?
3
Are these lines parallel?
t
a
b
If a transversal is added to the picture, what
information would tell you these lines are
parallel. (There are four different things you
can pick.)
4
Angles that can be used to show parallel lines
  • Alternate exterior angles
  • Alternate interior angles
  • Corresponding angles
  • Same side interior angles that add to 180

5
List the pair of parallel lines. How do you know
the lines are parallel?
a ll b by alt. int. angles are congruent
b ll c by corresponding angles are congruent
a ll c by alt. int. angles are congruent
6
Converse of Corresponding Angles Postulate
If two lines are cut by a transversal so that a
pair of corresponding angles are congruent, then
the lines are parallel.
Page 207
7
Euclids Postulate
  • This is one of Euclids five original postulates
    from 300 BC. Postulate 2.1 and Theorem 2.10 are
    similar to two of Euclids other postulates.

Page 208
8
Page 208
9
A contractor wants to guarantee that the new
street she is marking of is parallel to Douglass
Street. She finds that the measure of angle 1 is
45. Give three different ways that she can use
angles to be sure that the new street is parallel
to Douglass Street.
Main St.
Douglass St.
1
2
3
4
New St.
5
10
  • 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.
11
  • 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.
12
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.
13
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.
Solve the Test Item ?WXP and ?ZYN are alternate
exterior angles. For line PQ to be parallel to
line MN, the alternate exterior angles must be
congruent. So m?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.
14
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.
Now use the value of x to find m?ZYN.
m?ZYN 7x 35 Original equation
7(15) 35 x 15 140 Simplify.
Answer m?ZYN 140
15
How can we show (prove) that lines are parallel?
  • By showing that alternate exterior angles,
    alternate interior, corresponding angles or
    same-side interior angles are congruent.

16
3-5 Assignment
  • Page 211, 6, 8-20 even
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