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Pairs of Lines - Transversal of Parallel Lines

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notes

Transversal intersects two parallel lines:

  • If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
  • If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal.
  • If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary
  • When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.

Line l intersects lines m and n. Therefore, line l is a transversal for lines m and n.

  • If a transversal intersects two parallel lines, then each pair of corresponding angles is equal,
    (i) ∠ 1 and ∠ 5 (ii) ∠ 2 and ∠ 6
    (iii) ∠ 4 and ∠ 8 (iv) ∠ 3 and ∠ 7

  • If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal,
    (i) ∠ 4 and ∠ 6 (ii) ∠ 3 and ∠ 5

  • Alternate exterior angles:
    (i) ∠ 1 and ∠ 7 (ii) ∠ 2 and ∠ 8

  • If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
    (i) ∠ 4 + ∠ 5 = 180° (ii) ∠ 3 + ∠ 6 = 180°.

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