Question

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

Answer 1

This is an example

Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. That means angle 1 = angle 5 as well. 

When a line intersects two parallel lines, the corresponding angles are equal. That is, if r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s. Angle 1 = Angle 5, Angle 2 = Angle 6, and so forth. Since we know angle 1 = angle 5, so from that you can see that r and s are parallel

Answer 2

Answer:

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

Step-by-step 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.