Question

suppose you draw a different transversal that intersects the same two parallel lines. do you think the angle relationships you discovered will still be true?
① no
② yes

Explanation:

Step1: Recall angle - relationship theorems for parallel lines

When two parallel lines are cut by a transversal, there are several angle - relationships: corresponding angles (equal), alternate interior angles (equal), alternate exterior angles (equal), and consecutive interior angles (supplementary). These relationships are based on the properties of parallel lines and transversals, not on the specific position of the transversal (as long as the lines are parallel).

Step2: Analyze the effect of a different transversal

If we draw a different transversal for the same two parallel lines, the fundamental angle - relationships (corresponding angles are equal, alternate interior angles are equal, consecutive interior angles are supplementary etc.) still hold. For example, if \(\angle1\) and \(\angle2\) are corresponding angles for one transversal, and \(\angle3\) and \(\angle4\) are corresponding angles for another transversal (with the same parallel lines), the measure of corresponding angles (or other angle - pairs based on the relationships) will follow the rules of parallel - line and transversal geometry.

Answer:

B. yes