Question

Which lines are parallel if m 3 = m 6?
Justify your answer.​

Answer 1

`r \parallel s` by the Converse of the Alternate Interiors Angles Theorem.

Explanation:

Remember that two lines are parallel if their angle of direction is the same.

So, in this case we know that
`m\angle 3 = m\angle 6`, where
`\angle 3` is the direction of
`r` and
`\angle 6` is the direction of
`s`.

Therefore,
`r \parallel s` by the Converse of the Alternate Interior Angles Theorem, which states that if two lines are cut by a transversal and the alternate interior angles are congruent, then those lines are parallel.