1. Given: ∠4 ≅ ∠6
Prove: a || b
Statements:
1. ∠4 ≅ ∠6 (Given)
2. ∠6 ≅ ∠2 (Vertical Angles Theorem)
3. ∠4 ≅ ∠2 (Transitive Property of Congruence)
4. a || b (Converse of Corresponding Angles Postulate)
2. Given: a || b
Prove: m∠2 + m∠3 = 180°
Statements:
1. a || b (Given)
2. m∠1 + m∠2 = 180° (Linear Pair Postulate)
3. ∠1 ≅ ∠3 (Corresponding Angles Postulate)
4. m∠1 = m∠3 (Definition of Congruent Angles)
5. m∠3 + m∠2 = 180° (Substitution Property)
3. Given: p || q, s || t
Prove: ∠1 ≅ ∠3
Statements:
1. p || q (Given)
2. ∠1 ≅ ∠2 (Corresponding Angles Postulate)
3. s || t (Given)
4. ∠2 ≅ ∠3 (Alternate Interior Angles Theorem)
5. ∠1 ≅ ∠3 (Transitive Property of Congruence)
Parent Tip: Review the logic above to help your child master the concept of parallel lines proof worksheet answers.
