Question

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

Explanation:

Step1: State the given

Line l and line m intersect

Step2: Apply linear - pair theorem

$\angle1$ is supplementary to $\angle2$ because they form a linear pair. Also, $\angle2$ is supplementary to $\angle3$ (linear pair theorem).

Step3: Apply linear - pair theorem again

$\angle3$ is supplementary to $\angle4$ as they form a linear pair. And $\angle2\cong\angle4$ (vertical angles are congruent).

Step4: Use congruent - supplements theorem

Since $\angle1$ and $\angle3$ are both supplementary to angles that are congruent ($\angle2$ and $\angle4$ respectively), by the congruent - supplements theorem, $\angle1\cong\angle3$.

Answer:

From left - to - right in the flowchart: Line l and line m intersect, $\angle2$ is supplementary to $\angle3$, $\angle3$ is supplementary to $\angle4$, $\angle1\cong\angle3$