Question

complete the proof showing ∠3≅∠6 by dragging the correct statement or reason into the correct place within the proof. statements reasons f || h given corresponding angles of two parallel lines cut by a transversal are congruent vertical angles are congruent ∠3≅∠6 property of congruence ∠1≅∠6 ∠2≅∠6 ∠1≅∠3 ∠2≅∠3 reflexive transitive

Explanation:

Step1: Identify corresponding - angle pair

Since \(f\parallel h\) (given), by the property that corresponding angles of two parallel lines cut by a transversal are congruent, we have \(\angle1\cong\angle6\).

Step2: Identify vertical - angle pair

We know that vertical angles are congruent. So, \(\angle1\cong\angle3\) because they are vertical angles.

Step3: Use transitive property

By the transitive property of congruence, if \(\angle1\cong\angle6\) and \(\angle1\cong\angle3\), then \(\angle3\cong\angle6\).

Answer:

Statements: \(\angle1\cong\angle6\), \(\angle1\cong\angle3\), \(\angle3\cong\angle6\)
Reasons: Corresponding angles of two parallel lines cut by a transversal are congruent, Vertical angles are congruent, Transitive property of congruence