Lesson 22: Parallel Lines

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Lesson 22 Parallel Lines

• Oct. 21, 2009

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Homework

• Prove Theorem 3-3 3-4
• Geometry, P 82, 17-21

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Do Now True or False. Find a counterexample if
it is false.

• Two lines are either intersecting or parallel.
• If two segments do not intersect, then it is
  possible that they are not parallel either.
• There is exactly one line that can be drawn
  through a given point that is not on a given line
  and parallel to the given line.

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Vocabulary

• Skew Lines are noncoplanar lines.
• They are neither parallel or intersecting.
• Parallel Lines are coplanar lines that never
  intersect. (m//n, arrowheads in diagram)
• Portions (segments and rays) of parallel
  lines are parallel.
• Extensions of parallel segments or rays are
  parallel.

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Parallel Postulate

• Euclids Fifth Postulate (300 BC) If two lines,
  when cut by another line, form two same-side
  interior angles whose measures sum to less than
  180, then the two lines, if extended
  indefinitely, intersect.
• Playfairs Axiom (1795) (an alternative
  formulation of Euclids parallel postulate)
  There is exactly one line that can be drawn
  through a given point that is not on a given line
  and parallel to the given line.

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Vocabulary

• Interior and Exterior Region
• Transversal is the line that intersects two or
  more lines in different points.
• Interior Angles and Exterior Angles
• Alternate Interior Angles (alt int lt)
• Same-side Interior Angles (s-s int lt)
• Corresponding Angles (cor lt)
• Alternate Exterior Angles (alt ext lt)
• Same-side Exterior Angles (s-s ext lt)

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Properties of Parallel Lines
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Properties of Parallel Lines

• Postulate 10 If two parallel lines are cut by a
  transversal, then two corresponding angles are
  congruent.
• Theorem 3-2 If two parallel lines are cut by a
  transversal, then two alternate interior angles
  are congruent.
• Theorem 3-3 If two parallel lines are cut by a
  transversal, then same-side interior angles are
  supplementary.
• Theorem 3-4 If a transversal is perpendicular to
  one of two parallel lines, then it is
  perpendicular to the other one also.

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How do we use the properties of parallel lines in
proofs?

• Given RS//TW, TS//WX
• Prove ?S ? ?W

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Another example

• Given m//n
• Find m ?ABC.