Question

1. in the figure, \\(m\angle 2 = m\angle 6\\). what theorem can be used to prove that line a and line b are

(1 point)

a converse of alternate exterior angles
b converse of corresponding angles
c converse of alternate interior angles
d converse of supplementary angles

Explanation:

Identify the given angle relationship

Using the Converse of Alternate Interior Angles Theorem knowledge point

$$ m\angle 2 = m\angle 6 $$

Determine the positions of the angles

The angles \(\angle 2\) and \(\angle 6\) are located on opposite sides of the transversal line and lie inside the two lines \(a\) and \(b\). This makes them alternate interior angles.

Apply the parallel line converse theorem

Using the Converse of Alternate Interior Angles Theorem knowledge point

$$ \text{If alternate interior angles are equal, then the lines are parallel: } a \parallel b $$

Answer:

• A Converse of Alternate Exterior Angles
• B Converse of Corresponding Angles
• C Converse of Alternate Interior Angles (Correct answer)
• D Converse of Supplementary Angles