Question

given: \\( \overline { r w } \cong \overline { w t } ; \overline { u w } \cong \overline { w s } \\)
prove: rstu is a parallelogram.

identify the steps that complete the proof.

Explanation:

Step1: Vertical angles theorem

Vertical angles are congruent. So, for $\angle SWR$ and $\angle UWT$ (vertical angles), $\angle SWR\cong\angle UWT$.

Step2: SAS (Side - Angle - Side) congruence criterion

We have $\overline{RW}\cong\overline{WT}$, $\angle SWR\cong\angle UWT$, and $\overline{UW}\cong\overline{WS}$. By the SAS (Side - Angle - Side) congruence criterion, $\triangle SWR\cong\triangle UWT$.

Step3: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Since $\triangle SWR\cong\triangle UWT$, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), $\angle WRS\cong\angle WTU$ and $\angle WSR\cong\angle WUT$.

Answer:

♣: vertical angles theorem; ♦: SAS; ♠: CPCTC