Question

Given the information, determine if lines n and p are parallel.

m∠8 = m∠4
Which of the following can be concluded based on the provided information?

A) Yes, n is parallel to p by the Converse of the Corresponding Angles Postulate.
B) Yes, n is parallel to p by the Converse of the Consecutive Interior Angles Theorem.
C) Yes, n is parallel to p by the Converse of the Alternate Exterior Angles Theorem.
D) Yes, n is parallel to p by the Converse of the Alternate Interior Angles Theorem.
E) No, the lines are NOT parallel."

Answer 1

To determine if lines n and p are parallel, we can use the Converse of the Alternate Interior Angles Theorem. If the alternate interior angles formed by two lines and a transversal are congruent, then the lines are parallel.

Step-by-step explanation:

To determine if lines n and p are parallel, we need to analyze the angles associated with these lines. The given information states that m∠8 = m∠4. In order to conclude if the lines are parallel, we can use the Converse of the Alternate Interior Angles Theorem. According to this theorem, if the alternate interior angles formed by two lines and a transversal are congruent, then the lines are parallel. Therefore, the correct answer is D) Yes, n is parallel to p by the Converse of the Alternate Interior Angles Theorem.