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Ch. 3 Parallel and perpendicular lines

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					        Chapter 3
Parallel and Perpendicular lines

   By: Jackson Mitchell and
     Madeleine Misterek
        3-1: Lines and Angles
Types of lines and planes: (pg. 146)
  Parallel lines
  Skew lines
  Perpendicular lines
  Parallel planes
Classifying Angles: (pg. 147)
  Corresponding
  Alternate interior angles
  Same side angles
  Alternate exterior angles
  3-2: Angles Formed by Parallel
      Lines and Transversals
Using the Corresponding Angles
Postulate (pg.155)
Alternate interior angles are
congruent
Alternate exterior angles are
congruent
Same side interior angles are
SUPPLEMENTARY
             (pg. 156)
Remember! The angles cannot be proven congruent
unless the lines are parallel. Look for: >>
       3-3: Proving Lines Parallel
Postulate/Theorem                  If two lines are cut by a
                                   transversal so that…
Converse of Corresponding Angles   A pair of corresponding angles are
                                   congruent
Converse of Alt. Interior angles   A pair of alternate interior angles
                                   are congruent
Converse of Alt. exterior angles   A pair of alternate exterior angles
                                   are congruent
Converse of Same Side Interior     A pair of same side interior angles
Angles                             are supplementary

                   Then the lines are PARALLEL!

                          Pgs. 162 and 163
      3-4:Perpendicular Lines
The shortest distance from a point to a line is the perpendicular
segment.
Writing Inequalities:
Write and solve an inequality for x.
(pg. 172)



Theorem:
3-4-1: Two lines form linear pair of congruent angles, lines are
perp.
Perpendicular Transversal Thm: A transversal is perpendicular to
one of 2 parallel lines, it is perp. to the other.
3-4-3: Two lines are perp. To the same line, the lines are
parallel to eachother.
(pg. 173)
Proving Properties of Lines       (pg. 173)
                            C
      A
                        B


  E
                    F                     D



                                   H
                G

 Given: <ABC=90°, AD II EH
 Prove: Line EH is perpendicular to BG
          3-5: Slopes of Lines
  Slope formula: y2-y1 (pg. 182)
                 x2-x1
Parallel Lines Theorem: Two lines are parallel if
  they have the same slope.
Perpendicular Lines Theorem: two lines are
  perpendicular if the product of their slopes is -1.
(pg. 184)

  Parallel: line 1 slope a/b, line 2 slope a/b
  Perpendicular: Line 2 slope a/b, line 2 slope –b/a
Common Mistake: Don’t
assume the lines are
perpendicular! They must
be exactly 90°. Check the
slope!
3-6: Lines in a Coordinate plane
  Point Slope form: y-y =m(x-x )
                       1       1


  Slope intercept form: y=mx+b
(pg. 190)
Graphing Lines:
  Same slope and y-intercept – coinciding lines
  Different slopes and intercepts – intersecting
  lines
  Same slope and different y-intercepts –
  parallel lines
(pg. 192)
Graphing:
y=2x+3 -----slope intercept form
Plot the point (0,3), then rise 2 and
  run one to find another point.
y+4=-3(x-2)-----point intercept form
The slope is -3 through the point (2,-
  4)
Plot the point (2,-4) and then rise -3
  and run 1 to find another point.
(pg. 191 and 192)
Solve for y to find slope intercept form, then tell whether
     the lines are parallel, intersecting or coinciding:

          X+4y=8, 5x=15y+7




                       (pg. 192)

				
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posted:8/25/2011
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