1. Given: a || b, c || d
Prove: ∠1 ≅ ∠11
1. a || b, c || d (Given)
2. ∠1 ≅ ∠5 (Corresponding angles postulate, since a || b and transversal c)
3. ∠5 ≅ ∠11 (Corresponding angles postulate, since c || d and transversal b)
4. ∠1 ≅ ∠11 (Transitive property of congruence)
2. Given: a || b, c || d
Prove: ∠6 ≅ ∠8
1. a || b, c || d (Given)
2. ∠6 ≅ ∠2 (Alternate interior angles theorem, since a || b and transversal d)
3. ∠2 ≅ ∠8 (Vertical angles theorem)
4. ∠6 ≅ ∠8 (Transitive property of congruence)
Classify each pair of angles as alternate interior angles, alternate exterior angles, same-side (consecutive) interior angles, or corresponding angles.
1. ∠1 and ∠5: Corresponding angles
2. ∠3 and ∠7: Corresponding angles
3. ∠5 and ∠9: Corresponding angles
4. ∠10T and ∠6: Alternate interior angles
5. ∠2 and ∠10: Alternate exterior angles
6. ∠10TT and ∠8: Same-side interior angles
7. ∠1 and ∠11: Corresponding angles
8. ∠3 and ∠8: Alternate interior angles
Parent Tip: Review the logic above to help your child master the concept of parallel lines and transversal worksheet.
