Question

a diagram is shown where pl intersects bh, kg, and bh. given: bh || rf and ∠pxb ≅ ∠ywg. prove: rf || kg. statements: 1. bh || rf; 2. ∠pxb ≅ ∠lyf; 3. ∠pxb ≅ ∠ywg; 4. ∠lyf ≅ ∠ywg; 5. rf || kg. reasons: 1. given; 2. if two parallel lines are intersected by a transversal, then the choose your answer. angles are choose your answer.; 3. choose your answer.; 4. choose your answer.; 5. if two lines and a transversal form choose your answer. angles that are congruent, then the lines are choose your answer.

Explanation:

Step1: Identify angle type for BH||RF

∠PXB and ∠LYF are corresponding angles (BH||RF, transversal PL).

Step2: State given congruence

∠PXB ≅ ∠YWG (given).

Step3: Apply transitive property

∠LYF ≅ ∠YWG (transitive from Steps 1 and 2).

Step4: Conclude RF||KG

∠LYF and ∠YWG are corresponding angles; congruent corresponding angles imply RF||KG.

Answer:

1. corresponding
2. Given
3. Transitive property of congruence
4. corresponding; parallel