Question

drag each label to the correct location on the chart. not all labels will be used.
given: ∠1 and ∠2 are supplementary
∠2 and ∠3 are supplementary
prove: ∠1 ≅ ∠3
complete the flow chart to show the proof.
statements | reasons

1. ∠1 and ∠2 are supplementary | 1. given
2. ∠2 and ∠3 are supplementary | 2. given
3. ∠1 ≅ ∠3 | 3. congruent supplements theorem

labels: congruent supplements theorem, congruent complements, vertical angles theorem, given

Explanation:

Step1: Match first given statement

Assign "given" to $\angle 1$ and $\angle 2$ are supplementary.

Step2: Match second given statement

Assign "given" to $\angle 2$ and $\angle 3$ are supplementary.

Step3: Apply congruent supplements theorem

Assign "congruent supplements theorem" to $\angle 1 \cong \angle 3$.
This theorem states that if two angles are supplementary to the same angle, they are congruent. Here, both $\angle 1$ and $\angle 3$ are supplementary to $\angle 2$, so they are congruent.

Answer:

1. For $\boldsymbol{\angle 1}$ and $\boldsymbol{\angle 2}$ are supplementary: Reason = given
2. For $\boldsymbol{\angle 2}$ and $\boldsymbol{\angle 3}$ are supplementary: Reason = given
3. For $\boldsymbol{\angle 1 \cong \angle 3}$: Reason = congruent supplements theorem