Question

prove: $angle 1 cong angle 3$
complete the proof
line l and line m intersect
$angle 2 cong angle 4$
$angle 3$ is supplementary to $angle 4$
$angle 1 cong angle 3$
$angle 2$ is supplementary to $angle 3$
given
$angle 1$ is supplementary to $angle 2$
linear pair theorem
linear pair theorem
congruent supplements theorem

Explanation:

Step1: Identify given premise

Line \( l \) and line \( m \) intersect

Step2: Apply Linear Pair Theorem

\( \angle 1 \) is supplementary to \( \angle 2 \)

Step3: Apply Linear Pair Theorem again

\( \angle 2 \) is supplementary to \( \angle 3 \)

Step4: Apply Congruent Supplements Theorem

\( \angle 1 \cong \angle 3 \)

Answer:

The filled proof flow is:

1. Given: Line \( l \) and line \( m \) intersect
2. Linear Pair Theorem: \( \angle 1 \) is supplementary to \( \angle 2 \)
3. Linear Pair Theorem: \( \angle 2 \) is supplementary to \( \angle 3 \)
4. Congruent Supplements Theorem: \( \angle 1 \cong \angle 3 \)