3.3 Proofs with Parallel Lines

∠1 ≅ ∠3

∠3 ≅ ∠5

∠1 ≅ ∠6

∠6 ≅ ∠5

Converse of the Alternate Interior AnglesTheorem

Converse of the Same-Side (Consecutive Interior) Angles Postulate

Converse of the Corresponding Angles Theorem

Cannot be proved parallel

Converse of the Corresponding Angles Theorem

Converse of the Alternate Interior Angles Theorem

Converse of the Alternate Exterior Angles Theorem

Converse of the Consecutive Interior(Same-Side Interior) Angles Theorem

Not Enough Information to Prove Parallel

The Converse of the Corresponding Angles Theorem

The converse of the Alternate Interior Angles Theorem

The converse of the Alternate Exterior Angles Theorem

The Converse of Consecutive Interior (Same-Side Interior) Angles Theorem

Not Enough Information to Prove Parallel

A

B

C

D

A

B

C

D

A

B

C

D

13

35

37

78

102

r is parallel to s by converse of Alternate Interior Angles Thm.

u is parallel to v by Converse of Corresponding Angles Thm

s is ⊥ u by Converse of Alternate Interior Angles Thm

v ⊥ r by Converse of Alternate Exterior Angles Thm

copying a segment

bisecting a segment

copying an angle

constructing a perpendicular

parallel

congruent

similar

perpendicular

a line through P parallel to line l

a line through P intersecting line l

a line through P congruent to line l

a line through P perpendicular to line l