Vertical angles theorem Transitive property of ≅ Corresponding angles converse Postulate m ||n Given ∠1 ≅∠3 ∠1 ≅∠2 ∠2 ≅∠3 ∠1 ≅∠2 ∠1 is a rt. angle ∠2 is a rt. angle m∠2 = 90° m∠1 = m∠2 Corresponding Angles Theorem Def. of ⟂ p⟂r Given p⟂q Def. of right angle Def. of ⟂ q || r Def. of right angle m∠1 = 90° Def. of ≅ Substitution Prop. of Equality Given Def. of Linear Pair g ||h Congruent Supplements Theorem ∠1 and ∠2 are supplementary ∠2 and ∠3 are supplementary ∠1 ≅∠3 Alternate Exterior Angles Converse Theorem Given Corresponding Angles Theorem Given ∠1 ≅∠2 ∠2≅∠ 3 ∠1 ≅∠3 Corresponding Angles Converse Postulate Given p || r q || s Transitive Property of ≅ Given Corresponding Angles Theorem ∠1 ≅∠2 ∠1 ≅∠3 Given ∠2 ≅∠3 Alternate Exterior Angles Theorem c || d a || b Transitive Property of ≅ a || b Given Alternate Interior Angles Theorem Same-Side Interior Angles Theorem ∠1 ≅∠2 Given Substitution Property of Equality ∠2 and∠3 are supplementary c || d ∠1 and∠4 are supplementary ∠3 ≅∠4 Vertical Angles Theorem b ||c ∠4 ≅∠8 Alternate Interior Angles Theorem Given ∠5 ≅∠6 Transitive Property of ≅ ∠5 ≅∠8 Given Transitive Property of ≅ ∠6 ≅∠8 Vertical Angles Theorem ∠4 ≅∠5