Question

drag each label to the correct location on the flowchart.
given: line l and line m intersect
prove: $angle 1 cong angle 3$
complete the proof.
$angle 2 cong angle 4$
line l and line m intersect
$angle 1 cong angle 3$
$angle 2$ is supplementary to $angle 3$
$angle 3$ is supplementary to $angle 4$
given
$angle 1$ is supplementary to $angle 2$
linear pair theorem
linear pair theorem
congruent supplements theorem

Explanation:

Step1: Identify given statement

The starting given information is the premise of the proof.
Given: Line $l$ and line $m$ intersect

Step2: Apply linear pair theorem (second)

Use the linear pair theorem on $\angle 2$ and $\angle 3$, which form a linear pair.
$\angle 2$ is supplementary to $\angle 3$

Step3: Apply congruent supplements theorem

Since $\angle 1$ is supplementary to $\angle 2$, and $\angle 2$ is supplementary to $\angle 3$, the congruent supplements theorem gives the final result.
$\angle 1 \cong \angle 3$

Answer:

1. First box (given): $\boldsymbol{\text{Line } l \text{ and line } m \text{ intersect}}$
2. Third box (linear pair theorem): $\boldsymbol{\angle 2 \text{ is supplementary to } \angle 3}$
3. Fourth box (congruent supplements theorem): $\boldsymbol{\angle 1 \cong \angle 3}$