Question

drag each label to the correct location on the flowchart. given: line l and line m intersect prove: ∠1 ≅ ∠3 complete the proof. line l and line m intersect; ∠3 is supplementary to ∠4; ∠1 ≅ ∠3; ∠2 ≅ ∠4; ∠2 is supplementary to ∠3 flowchart steps: first box (given) → ∠1 is supplementary to ∠2 (linear pair theorem) → second box (linear pair theorem) → third box (congruent supplements theorem) reset next

Explanation:

Step1: Identify the given

The first box is for the given information, so we use "Line \( l \) and line \( m \) intersect".

Step2: Find \( \angle 2 \)'s supplement

By linear pair theorem, \( \angle 2 \) and \( \angle 3 \) form a linear pair, so \( \angle 2 \) is supplementary to \( \angle 3 \).

Step3: Apply congruent supplements theorem

We know \( \angle 1 \) is supplementary to \( \angle 2 \) and \( \angle 2 \) is supplementary to \( \angle 3 \). By the congruent supplements theorem, \( \angle 1 \cong \angle 3 \).

Answer:

1. First box: Line \( l \) and line \( m \) intersect
2. Third box: \( \angle 2 \) is supplementary to \( \angle 3 \)
3. Fourth box: \( \angle 1 \cong \angle 3 \) (by congruent supplements theorem)