Question

given: a || b
∠6 ≅ ∠2
prove: a || c
1 a || b
given
2 ∠6 ≅ ∠2
given
3 validate
reason?

Explanation:

Step1: Use the property of parallel lines

Since \(a\parallel b\) (given), and if two parallel lines are cut by a transversal, then corresponding angles are equal. But here, we can use the property of alternate - interior angles. When \(a\parallel b\), \(\angle6\cong\angle4\) (alternate - interior angles). Also, \(\angle2\cong\angle4\) (vertical angles). By the transitive property of congruence (if \(A\cong B\) and \(B\cong C\), then \(A\cong C\)), if \(\angle6\cong\angle4\) and \(\angle2\cong\angle4\), then \(\angle6\cong\angle2\).

Step2: Use the converse of parallel lines

If \(\angle6\cong\angle2\), then \(a\parallel c\) (by the converse of the corresponding angles postulate. If two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel).

Answer:

The reason for step 3 is "Transitive property of congruence and converse of corresponding angles postulate"