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

because of the

. therefore, ∠mvb≅∠vwg because of the

:: th || mp :: th || cr :: cr || nz :: nz || mp

Explanation:

Step1: Identify vertical - angle relationship

$\angle MVR$ and $\angle MVB$ are a linear - pair, and $\angle GWP$ and $\angle VWG$ are a linear - pair. Also, vertical angles are equal. Since $\angle MVR\cong\angle GWP$, and $\angle MVR$ and $\angle MVB$ form a linear pair, $\angle GWP$ and $\angle VWG$ form a linear pair.

Step2: Use linear - pair and congruence properties

If two angles are congruent, and their supplements (angles that form a linear pair with them) are considered, the supplements of congruent angles are congruent. $\angle MVB$ is the supplement of $\angle MVR$ and $\angle VWG$ is the supplement of $\angle GWP$. So, $\angle MVB\cong\angle VWG$ by the Congruent Supplements Theorem.

Answer:

The missing statements and reasons:

1. $\angle MVR$ and $\angle MVB$ are supplementary, $\angle GWP$ and $\angle VWG$ are supplementary (Definition of linear - pair).
2. Supplements of congruent angles are congruent (Congruent Supplements Theorem).