given: $\overline{rw} \cong \overline{wt}$; $\overline{uw} \cong \overline{ws}$\
prove: rstu is a parallelogram.\
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identify the steps that complete the proof.\
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statements\
1. $\overline{rw} \cong \overline{wt}$; $\overline{uw} \cong \overline{ws}$\
2. $\angle swr$ and $\angle uwt$ are vertical angles\
3. $\angle swr \cong \angle uwt$\
4. $\triangle swr \cong \triangle uwt$\
5. $\angle wrs \cong \angle wtu$, $\angle wsr \cong \angle wut$\
6. $\overline{ru} \parallel \overline{st}$, $\overline{ut} \parallel \overline{rs}$\
7. rstu is a parallelogram\
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reasons\
1. given\
2. def. of vertical angles\
3. $\boldsymbol{\downarrow}$\
4. $\boldsymbol{\downarrow}$\
5. $\boldsymbol{\downarrow}$\
6. converse of alt. interior angles theorem\
7. def. of a parallelogram

Question

Accepted Answer

# Explanation:
## Step 1: Reason for $\angle SWR \cong \angle UWT$
Vertical angles are congruent. So the reason is "vertical angles are congruent".
## Step 2: Reason for $	riangle SWR \cong 	riangle UWT$
We have $\overline{RW} \cong \overline{WT}$, $\overline{UW} \cong \overline{WS}$ (given) and $\angle SWR \cong \angle UWT$ (proven in step 3). So by the Side - Angle - Side (SAS) congruence criterion, $	riangle SWR \cong 	riangle UWT$. The reason is "SAS congruence criterion".
## Step 3: Reason for $\angle WRS \cong \angle WTU$, $\angle WSR \cong \angle WUT$
Corresponding parts of congruent triangles are congruent (CPCTC). Since $	riangle SWR \cong 	riangle UWT$, their corresponding angles are congruent. So the reason is "CPCTC".

# Answer:
3. vertical angles are congruent
4. SAS congruence criterion
5. CPCTC

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QUESTION IMAGE

Question

Explanation:

Step 1: Reason for $\angle SWR \cong \angle UWT$

Step 2: Reason for $\triangle SWR \cong \triangle UWT$

Step 3: Reason for $\angle WRS \cong \angle WTU$, $\angle WSR \cong \angle WUT$

Answer: