5. Alternate interior angles: ∠1 ≅ ∠5; ∠5 ≅ ∠7 and ∠4 ≅ ∠6
6. Alternate exterior angles: ∠3 ≅ ∠9 and ∠2 ≅ ∠8
7. Corresponding angles: ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠5 ≅ ∠9; ∠4 ≅ ∠8 and ∠1 ≅ ∠3
8. Vertical angles: ∠2 ≅ ∠4; ∠3 ≅ ∠5; ∠7 ≅ ∠9; and ∠6 ≅ ∠8 .
9. ∠1 and ∠7.
What are the Special Pairs of Angles Formed by a Transversal and Parallel Lines?
If two lines that are cut across by a transversal are parallel, the following special angles are formed:
- Corresponding angles which are congruent: they share the same corner and lie along a transversal.
- Alternate interior angles which are congruent: they lie opposite each other along the transversal inside each parallel lines.
- Alternate exterior angles which are congruent: they lie opposite each other along the transversal outside each parallel lines.
- Vertical Angles which are congruent: they are directly opposite each other and share the same vertex but they are non-adjacent.
Given the image given, we can identify the following special angles:
5. Alternate interior angles: ∠1 ≅ ∠5; ∠5 ≅ ∠7 and ∠4 ≅ ∠6
6. Alternate exterior angles: ∠3 ≅ ∠9 and ∠2 ≅ ∠8
7. Corresponding angles: ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠5 ≅ ∠9; ∠4 ≅ ∠8 and ∠1 ≅ ∠3
8. Vertical angles: ∠2 ≅ ∠4; ∠3 ≅ ∠5; ∠7 ≅ ∠9; and ∠6 ≅ ∠8 .
9. ∠1 ≅ ∠3 and ∠3 ≅ ∠7. So the two angles would be ∠1 ≅ ∠7.
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