Question

Need help asap. Consider the diagram.

Answer 1

Question:

Given that r||s and q is a transversal, we know that  by the [________].

Answer:

alternate interior angles theorem

Answer 2

ANSWER

alternate interior angles theorem

EXPLANATION

According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.

From the above diagram line r is parallel to line s, therefore

$\angle \: 3 \cong \angle6$

and

$\angle \: 4\cong \angle5$

because they are alternate interior angles.

See attachment for how to spot alternate interior angles.