Question

Use the proof diagram to complete the question. State the missing reason in this proof for the letter given.

Answer 1

Answer:

See below.

Step-by-step explanation:

We know that $\angle 1\cong\angle 5$ and we want to prove that $p\parallel r$.

  Statements                                         Reasons

1) $\angle 1\cong \angle 5$                                               Given

2) $\angle 4\cong \angle 1$                                              A) Vertical Angles Are Congruent

3) $\angle 4\cong \angle5$                                             B) Substitution Property

4) $p\parallel r$                                                   C) Alternate Interior Angles Converse*

*We know that alternate interior angles are congruent when two parallel lines are cut by a transversal. So, the converse states that if the two alternate interior angles are congruent, the the two lines must be parallel.

Further Notes:

I'm not sure why they did more than necessary. Since $\angle 1\cong \angle 5$, they are corresponding angles. Then by the Corresponding Angles Converse, p must be parallel to r.