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Pairs of Lines - Angles Made by a Transversal

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notes

1. Pairs Of Angles:

a. Corresponding angles:

  • Corresponding angles have distinct vertex points,

  • Corresponding angles lie on the same side of the transversal and

  • Corresponding angles one angle is interior and the other is exterior.

  • Pairs of Corresponding angles:

The F-shape stands for corresponding angles:

b. Alternate angles:

(i) Alternate interior angles:

  • Alternate interior angles have different vertices

  • Alternate interior angles are on opposite sides of the transversal and

  • Alternate interior angles lie ‘between’ the two lines i.e., both angles are interior.

(ii) Alternate exterior angles:

  • Alternate exterior angles have different vertices
  • Alternate exterior angles are on opposite sides of the transversal
  • Alternate exterior angles are not lain ‘between’ the two lines i.e., both angles are exterior.

The Z-shape stands for alternate angles:

C. Consecutive Interior Angles:

  • The pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles.

  • If the transversal cuts across parallel lines then the interior angles are supplementary (add to 180°) than you can conclude the lines are parallel.

2. Pairs of Lines - Angles Made by a Transversal:

  • A transversal gives rise to several types of angles.
  • Line l intersects lines m and n at points P and Q respectively. Therefore, line l is a transversal for lines m and n.
  • ∠ 1, ∠ 2, ∠7, and ∠8 are called exterior angles, while ∠3, ∠4, ∠5, and ∠6 are called interior angles.
  • Interior angles on the same side of the transversal are also referred to as consecutive interior angles or allied angles or co-interior angles.

(a) Corresponding angles:
(i) ∠ 1 and ∠ 5 (ii) ∠ 2 and ∠ 6
(iii) ∠ 4 and ∠ 8 (iv) ∠ 3 and ∠ 7

(b) Alternate interior angles:
(i) ∠ 4 and ∠ 6 (ii) ∠ 3 and ∠ 5

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

(d) Interior angles on the same side of the transversal:
(i) ∠ 4 and ∠ 5 (ii) ∠ 3 and ∠ 6.

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