Question

given \\(p \parallel q\\) and \\(t\\) is a transversal, which of the following justifies \\(\angle 3 \cong \angle 6\\)?

a. corresponding angles postulate
b. alternate interior angles theorem
c. consecutive interior angles theorem
d. alternate exterior angles theorem

Explanation:

Identify the given lines and transversal

Using the Parallel Line Angles and Transversal Lines knowledge points

• Two parallel lines \(P\) and \(Q\) are intersected by a transversal line \(T\).
• This intersection creates eight distinct angles labeled 1 through 8.

Analyze the positions of the given angles

Using the Alternate Interior Angles and Transversal Lines knowledge points

• We are analyzing the relationship between \(\angle 3\) and \(\angle 6\).
• Both angles lie in the interior region between the parallel lines \(P\) and \(Q\).
• \(\angle 3\) is on the left side of the transversal \(T\), while \(\angle 6\) is on the right side.

Determine the justifying theorem

Using the Alternate Interior Angles knowledge point

• Since \(\angle 3\) and \(\angle 6\) are on opposite sides of the transversal and inside the parallel lines, they are alternate interior angles.
• The theorem stating that alternate interior angles are equal when lines are parallel is the Alternate Interior Angles Theorem.

Answer:

• A. Corresponding Angles Postulate
• B. Alternate Interior Angles Theorem (Correct answer)
• C. Consecutive Interior Angles Theorem
• D. Alternate Exterior Angles Theorem