Proving Lines Parallel

No

Yes, corresponding angles are congruent

Yes, consecutive interior angles are congruent

Yes, Alternate interior angles are congruent

Line e and line f

Line a and line b

Line e and line a

Line f and line b

If two lines are parallel to the same line, then they are parallel to each other.

If two lines are perpendicular to the same line then they are parallel to each other.

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

Alternate Interior

Alternate Exterior

 Correpsonding

Vertical Angles

43

37

143

37

No

Yes, Corresponding angles are congruent

Yes, Alternate Interior angles are congruent

Yes, Alternate Exterior angles are congruent

Alternate Interior

Alternate Exterior

Corresponding

Vertical Angles

Reflexive Property of congruence

Substitution

Transitive Property of equality

Transitive Property of congruence

No

Yes, Corresponding angles are congruent

Yes, Alternate Interior angles are congruent

Yes, Alternate Exterior angles are congruent

$$m\parallel n$$ because Alternate Interior angles are congruent

$$p\parallel q$$ because Alternate Interior angles are congruent

$$m\parallel n$$ because Consecutive Interior angles are congruent

Neither pair of lines is parallel