Question

∠2 and ∠3 are supplementary 2. given

1. ∠1 ≅ ∠3 3. congruent supplements theorem

complete the flow chart to show the proof
congruent complements given vertical angles theorem congruent supplements theorem
∠1 and ∠2 are supplementary ∠1 = ∠3
∠2 and ∠3 are supplementary

Explanation:

Step1: Assign reason to first statement

Match "∠1 and ∠2 are supplementary" to "given"

Step2: Assign reason to second statement

Match "∠2 and ∠3 are supplementary" to "vertical angles theorem" (since vertical angles' supplements relate here, and this establishes the pair)

Step3: Assign reason to conclusion

Match "∠1 ≅ ∠3" to "congruent supplements theorem"

Answer:

• Under $\boldsymbol{\angle 1 \text{ and } \angle 2 \text{ are supplementary}}$: $\boldsymbol{\text{given}}$
• Under $\boldsymbol{\angle 2 \text{ and } \angle 3 \text{ are supplementary}}$: $\boldsymbol{\text{vertical angles theorem}}$
• Next to $\boldsymbol{\angle 1 \cong \angle 3}$: $\boldsymbol{\text{congruent supplements theorem}}$