Question

1. which statement proves line c is parallel to line d? a) < 1 ≅ < 3 b) < 1 ≅ < 10 c) < 4 ≅ < 12 d) < 4 ≅ < 16

Explanation:

Step1: Recall the Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then corresponding angles are congruent. Conversely, if corresponding angles are congruent, then the lines are parallel.

Step2: Analyze each option

• Option A: $\angle1$ and $\angle3$ are not corresponding angles for lines \(c\) and \(d\).
• Option B: $\angle1$ and $\angle10$ are not corresponding angles for lines \(c\) and \(d\).
• Option C: $\angle4$ and $\angle12$ are not corresponding angles for lines \(c\) and \(d\).
• Option D: $\angle4$ and $\angle16$ are corresponding angles. If $\angle4\cong\angle16$, by the Corresponding Angles Postulate, line \(c\) is parallel to line \(d\).

Answer:

D. $\angle4\cong\angle16$