complete the two - column proof. given: ∠dbv≅∠mpg and ∠tbd≅∠wfb prove: ∠rfp≅∠mpf
statement reason
∠dbv≅∠mpg given
5. ∠tbd≅∠wfb 5. given
6. (overline{tv}paralleloverline{wr}) 6. if corresponding
7. (overline{tw}paralleloverline{mc}) 7. if alternate
8. (overline{wr}paralleloverline{mc}) 8. transitive
9. ∠tbd≅∠mpf 9.
10. 10.
write the statements and reasons in the correct order in the two - column proof. ∠pfr≅∠mpf given
∠tbd≅∠wfb transitive property of congruence
∠pfr≅∠tbd if two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent.
∠tbd≅∠mpf if two parallel lines are intersected by a transversal, then the corresponding angles are congruent.
(overline{tv}paralleloverline{mc}) if alternate exterior angles are congruent, then the two lines that are intersected by a transversal are parallel.
(overline{tv}paralleloverline{wr}) if corresponding angles are congruent, then the two lines that are intersected by a transversal are parallel.

Question

Accepted Answer

# Explanation:
## Step1: State given angles
$\angle DBV\cong\angle MPG$ (Given) and $\angle TBD\cong\angle WFB$ (Given)
## Step2: Determine parallel lines from corresponding - congruent angles
Since $\angle TBD\cong\angle WFB$, then $\overline{TV}\parallel\overline{WR}$ (If corresponding angles are congruent, then the two lines that are intersected by a transversal are parallel)
## Step3: Determine another set of parallel lines from alternate - congruent angles
Since $\angle DBV\cong\angle MPG$, then $\overline{TW}\parallel\overline{MC}$ (If alternate exterior angles are congruent, then the two lines that are intersected by a transversal are parallel)
## Step4: Use transitive property for parallel lines
Since $\overline{TW}\parallel\overline{MC}$ and $\overline{TV}\parallel\overline{WR}$, then $\overline{WR}\parallel\overline{MC}$ (Transitive property of parallel lines)
## Step5: Find congruent angles from parallel lines
Since $\overline{WR}\parallel\overline{MC}$ and they are intersected by a transversal, $\angle TBD\cong\angle MPF$ (If two parallel lines are intersected by a transversal, then the corresponding angles are congruent)
## Step6: Use transitive property of congruence
Since $\angle TBD\cong\angle WFB$ and $\angle TBD\cong\angle MPF$, and $\angle PFR\cong\angle WFB$ (Vertical angles are congruent), then $\angle PFR\cong\angle MPF$ (Transitive Property of Congruence)

# Answer:
| Statement | Reason |
|--|--|
| $\angle DBV\cong\angle MPG$ | Given |
| $\angle TBD\cong\angle WFB$ | Given |
| $\overline{TV}\parallel\overline{WR}$ | If corresponding angles are congruent, then the two lines that are intersected by a transversal are parallel |
| $\overline{TW}\parallel\overline{MC}$ | If alternate exterior angles are congruent, then the two lines that are intersected by a transversal are parallel |
| $\overline{WR}\parallel\overline{MC}$ | Transitive property of parallel lines |
| $\angle TBD\cong\angle MPF$ | If two parallel lines are intersected by a transversal, then the corresponding angles are congruent |
| $\angle PFR\cong\angle MPF$ | Transitive Property of Congruence |

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QUESTION IMAGE

Question

Explanation:

Step1: State given angles

Step2: Determine parallel lines from corresponding - congruent angles

Step3: Determine another set of parallel lines from alternate - congruent angles

Step4: Use transitive property for parallel lines

Step5: Find congruent angles from parallel lines

Step6: Use transitive property of congruence

Answer:

Statement	Reason
$\angle TBD\cong\angle WFB$	Given
$\overline{TV}\parallel\overline{WR}$	If corresponding angles are congruent, then the two lines that are intersected by a transversal are parallel
$\overline{TW}\parallel\overline{MC}$	If alternate exterior angles are congruent, then the two lines that are intersected by a transversal are parallel
$\overline{WR}\parallel\overline{MC}$	Transitive property of parallel lines
$\angle TBD\cong\angle MPF$	If two parallel lines are intersected by a transversal, then the corresponding angles are congruent
$\angle PFR\cong\angle MPF$	Transitive Property of Congruence