Question

question 9. lines f and h are parallel and intersected by line q, as shown. 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

Explanation:

Step1: Identify corresponding angles

Since \(f\parallel h\) and \(q\) is a transversal, \(\angle3\) and \(\angle7\) are corresponding - angles. So \(\angle3\cong\angle7\) because corresponding angles of two parallel lines cut by a transversal are congruent.

Step2: Use vertical - angle property

\(\angle7\) and \(\angle6\) are vertical angles. By the vertical - angle theorem, vertical angles are congruent, so \(\angle7\cong\angle6\).

Step3: Apply transitive property of congruence

If \(\angle3\cong\angle7\) and \(\angle7\cong\angle6\), then by the transitive property of congruence (\(a\cong b\) and \(b\cong c\) implies \(a\cong c\)), \(\angle3\cong\angle6\).

Answer:

1. Statements: \(\angle3\cong\angle7\); Reasons: Corresponding angles of two parallel lines cut by a transversal are congruent
2. Statements: \(\angle7\cong\angle6\); Reasons: Vertical angles are congruent
3. Statements: \(\angle3\cong\angle6\); Reasons: Transitive property of congruence