Question

select the correct answer from each drop - down menu.
given: ( a parallel b )
prove: ( angle 1 cong angle 7 )
complete the proof.

Explanation:

Step1: Use corresponding angles theorem

Since \(a\parallel b\), by the corresponding angles theorem, \(\angle1\cong\angle5\).

Step2: Use vertical angles theorem

\(\angle5\) and \(\angle7\) are vertical angles. By the vertical angles theorem, \(\angle5\cong\angle7\).

Step3: Use transitive property of congruence

If \(\angle1\cong\angle5\) and \(\angle5\cong\angle7\), then by the transitive property of congruence, \(\angle1\cong\angle7\).

Answer:

1. \(\angle1\cong\angle5\) - corresponding angles theorem; 3. \(\angle5\cong\angle7\) - vertical angles theorem; 4. \(\angle1\cong\angle7\) - transitive property of congruence.