Question

complete the paragraph proof. given: ∠mvr≅∠gwp prove: ∠mvb≅∠vwg an incomplete paragraph proof shown includes some statements and reasons to prove ∠mvb≅∠vwg. complete each missing statement. since it is given that ∠mvr≅gwp, then
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because of the
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. therefore, ∠mvb≅∠vwg because of the
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Explanation:

Step1: Identify vertical - angle pairs

$\angle MVR$ and $\angle MVB$ are vertical angles, $\angle GWP$ and $\angle VWG$ are vertical angles.

Step2: Recall vertical - angle property

Vertical angles are congruent. So, $\angle MVR\cong\angle MVB$ and $\angle GWP\cong\angle VWG$.

Step3: Use the transitive property

Since $\angle MVR\cong\angle GWP$ (given) and $\angle MVR\cong\angle MVB$, $\angle GWP\cong\angle VWG$, by the transitive property of congruence, $\angle MVB\cong\angle VWG$.

Answer:

Since it is given that $\angle MVR\cong\angle GWP$, then $\angle MVR\cong\angle MVB$ and $\angle GWP\cong\angle VWG$ because vertical angles are congruent. Therefore, $\angle MVB\cong\angle VWG$ because of the transitive property of congruence.