Write a flowchart proof. Given: <2 and <3 are supplementary. Prove: <1 and <3 are supplementary

To prove that <1 and <3 are supplementary, we will create a flowchart proof.

Here is a step-by-step process for constructing the flowchart proof:

1. Start at the top of the flowchart with the given statement: <2 and <3 are supplementary.
2. Draw an arrow pointing downwards and label it "If" to indicate the start of a conditional statement.
3. Write "<1 = <2" below the "If" arrow to represent the statement that <1 is equal to <2.
4. Draw an arrow pointing downwards from the "If" statement and label it "Then" to indicate the next step.
5. Write "<1 and <3 are supplementary" below the "Then" arrow to represent the statement we want to prove.
6. Draw a final arrow pointing to the end of the flowchart to indicate the completion of the proof.
7. Write "Proof Complete" at the end of the flowchart.

The flowchart proof should look like this:

```
____________________________
| |
Start -> | <2 and <3 are supplementary |
|____________________________|
|
V
If
|
V
<1 = <2
|
V
Then
|
V
<1 and <3 are supplementary
|
V
Proof Complete
```

By using this flowchart proof, we can visually represent and organize the logical steps needed to prove that <1 and <3 are supplementary given that <2 and <3 are supplementary.