Question

1. given: ∠1≅∠5,∠3≅∠4 prove: l || v statements reasons

Explanation:

Step1: State given information

$\angle1\cong\angle5,\angle3\cong\angle4$ (Given)

Step2: Use corresponding - angle postulate

If two lines are cut by a transversal and corresponding angles are congruent, the lines are parallel. $\angle1$ and $\angle5$ are corresponding angles. Since $\angle1\cong\angle5$, by the corresponding - angles postulate, we can start to build our proof for parallel lines.

Step3: Consider vertical angles

$\angle3$ and $\angle5$ are vertical angles, so $\angle3\cong\angle5$ (Vertical angles are congruent).

Step4: Use transitive property

Since $\angle3\cong\angle4$ (given) and $\angle3\cong\angle5$ (vertical angles), by the transitive property of congruence, $\angle4\cong\angle5$.

Step5: Prove parallel lines

$\angle4$ and $\angle5$ are alternate - interior angles. If alternate - interior angles are congruent, then the two lines are parallel. So, $l\parallel v$.

Answer:

Statements:

1. $\angle1\cong\angle5,\angle3\cong\angle4$
2. $\angle3\cong\angle5$
3. $\angle4\cong\angle5$
4. $l\parallel v$

Reasons:

1. Given
2. Vertical angles are congruent
3. Transitive property of congruence
4. Alternate - interior angles congruent, lines parallel