# Parallel and Perpendicular Proofs Level A ```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&deg;
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&deg;
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
```