When a transversal intersects two parallel lines, it creates specific angle relationships. Here's a breakdown of the key theorems:

  1. Alternate Interior Angles Theorem 📐

    • These angles are equal in measure.
    Alternate_Interior_Angles
    - Example: If line *l* ∥ line *m* and a transversal *t* cuts them, ∠3 ≅ ∠6 and ∠4 ≅ ∠5.

  2. Corresponding Angles Theorem 🔄

    • Angles in matching positions are congruent.
    Corresponding_Angles
    - Example: ∠1 ≅ ∠5, ∠2 ≅ ∠6, etc.

  3. Same-Side Interior Angles Theorem 📏

    • These angles are supplementary (sum to 180°).
    Same_Side_Interior_Angles
    - Example: ∠3 + ∠5 = 180°.

For deeper exploration, check our geometry section or angle relations proofs. 🌐