Final Answer:
1. ∠1 ≅ ∠5 — Given
2. ∠3 ≅ ∠7 — Corresponding angles postulate (since lines are parallel and cut by a transversal)
3. ∠2 ≅ ∠6 — Corresponding angles postulate
4. ∠4 ≅ ∠8 — Corresponding angles postulate
5. ∠1 ≅ ∠3 — Vertical angles theorem
6. ∠2 ≅ ∠4 — Vertical angles theorem
7. ∠5 ≅ ∠7 — Vertical angles theorem
8. ∠6 ≅ ∠8 — Vertical angles theorem
Second diagram (with intersecting lines and parallel lines):
1. ∠A ≅ ∠D — Alternate interior angles (parallel lines cut by transversal)
2. ∠B ≅ ∠C — Alternate interior angles
3. ∠A ≅ ∠C — Vertical angles
4. ∠B ≅ ∠D — Vertical angles
5. ∠A + ∠B = 180° — Linear pair (adjacent angles on a straight line)
Parent Tip: Review the logic above to help your child master the concept of proofs with parallel lines worksheet.
