Question

given: ( l parallel m ); ( angle 1 cong angle 3 ) prove: ( p parallel q ) complete the missing parts of the paragraph proof. we know that angle 1 is congruent to angle 3 and that line ( l ) is parallel to line ( m ) because it is given. we see that angle 2 is congruent to angle 3 by the alternate interior angles theorem. therefore, angle 1 is congruent to angle 2 by the transitive property. so, we can conclude that lines ( p ) and ( q ) are parallel by the

Explanation:

The problem is about proving two lines are parallel. After establishing angle - angle congruence (∠1 ≅ ∠2), the converse of the corresponding angles theorem is used. This theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. Here, ∠1 and ∠2 are corresponding angles (formed by transversal cutting lines \(p\) and \(q\)), and since ∠1 ≅ ∠2, we apply the converse of the corresponding angles theorem.

Answer:

corresponding angles theorem