1.4.1 Parallel Lines and Transversals

1.4.1 Parallel Lines and Transversals

• 1.
  Parallel Lines &Transversals The student is able to (I can): • Identify parallel lines, perpendicular lines, skew lines, and parallel planes • Identify – Transversals – Corresponding angles – Alternate Interior Angles – Alternate Exterior Angles – Consecutive Interior Angles
• 2.
  parallelparallelparallelparallel lineslineslineslines –coplanar lines that do not intersect perpendicularperpendicularperpendicularperpendicular lineslineslineslines – two coplanar lines that intersect at right angles (90˚) m n m n f g f ⊥ g ⊥ means “perpendicular” means “parallel”
• 3.
  skewskewskewskew lineslineslineslines –noncoplanar lines that do not intersect parallelparallelparallelparallel planesplanesplanesplanes – planes that do not intersect R S Plane R Plane S
• 4.
  transversaltransversaltransversaltransversal – aline that intersects two coplanar lines at two different points r s t
• 5.
  correspondingcorrespondingcorrespondingcorresponding anglesanglesanglesangles –angles that lie on the same side of the transversal t, on the same sides of lines r and s Example: ∠1 and ∠5 CorrespondingCorrespondingCorrespondingCorresponding anglesanglesanglesangles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent. 87 6 5 4 3 1 2 ∠1 ≅ ∠5 ∠2 ≅ ∠6 ∠3 ≅ ∠7 ∠4 ≅ ∠8 t s r
• 6.
  alternate interioralternate interioralternateinterioralternate interior anglesanglesanglesangles – angles that lie on opposite sides of the transversal t, between lines r and s Example: ∠2 and ∠7 or ∠4 and ∠5 Alternate interior anglesAlternate interior anglesAlternate interior anglesAlternate interior angles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent. r s t interior 8 7 6 5 4 3 1 2 ∠2 ≅ ∠7 ∠4 ≅ ∠5
• 7.
  alternate exterioralternate exterioralternateexterioralternate exterior anglesanglesanglesangles – angles that lie on opposite sides of the transversal t, outside lines r and s Example: ∠1 and ∠8 Alternate exterior anglesAlternate exterior anglesAlternate exterior anglesAlternate exterior angles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent. r s t exterior exterior 8 7 6 5 4 3 1 2 ∠1 ≅ ∠8 ∠4 ≅ ∠5
• 8.
  consecutive interiorconsecutive interiorconsecutiveinteriorconsecutive interior anglesanglesanglesangles – angles that lie on the same side of the transversal t, between the lines r and s. Example: ∠3 and ∠5 ConsecutiveConsecutiveConsecutiveConsecutive interior anglesinterior anglesinterior anglesinterior angles of parallel lines areof parallel lines areof parallel lines areof parallel lines are supplementary.supplementary.supplementary.supplementary. r s t interior 87 65 43 1 2 m∠3 + m∠5 = 180˚ m∠4 + m∠6 = 180˚
• 9.
  consecutiveconsecutiveconsecutiveconsecutive exterior anglesexterioranglesexterior anglesexterior angles – angles that lie on the same side of the transversal t, outside the lines r and s. Example: ∠2 and ∠8 ConsecutiveConsecutiveConsecutiveConsecutive exterior anglesexterior anglesexterior anglesexterior angles of parallel lines areof parallel lines areof parallel lines areof parallel lines are supplementary.supplementary.supplementary.supplementary. r s t interior 87 65 43 1 2 m∠1 + m∠7 = 180˚ m∠2 + m∠8 = 180˚
• 10.
  1. Find themeasures of the numbered angles if m∠8 = 125˚ 2. List each angle pair corresponding angles alt. interior angles alt. exterior angles consecutive interior angles 1 2 3 8 4 5 6 7 Examples
• 11.
  1. Find themeasures of the numbered angles if m∠8 = 125˚ m∠1 = 125˚; m∠2 = 55˚; m∠3 = 55˚; m∠4 = 125˚; m∠5 = 55˚; m∠6 = 55˚; m∠7 = 125˚ 2. List each angle pair corresponding angles ∠1 & ∠4; ∠2 & ∠5; ∠3 & ∠6; ∠8 & ∠7 alt. interior angles ∠3 & ∠5; ∠8 & ∠4 alt. exterior angles ∠1 & ∠7; ∠2 & ∠6 consecutive interior angles ∠3 & ∠4; ∠8 & ∠5 1 2 3 8 4 5 6 7 Examples