Question

2-2 additional practice proving lines parallel use the figure for exercises 1 - 4. using the given information, which lines can you conclude are parallel? state the theorem or postulate that justifies each answer. 1. ∠1≅∠4 2. ∠2≅∠3 3. ∠6≅∠7 4. m∠5 + m∠8 = 180°

Explanation:

Step1: Identify corresponding - angles

Corresponding - angles are equal when lines are parallel. For $\angle1\cong\angle4$, since $\angle1$ and $\angle4$ are corresponding angles, by the Corresponding Angles Postulate, we can conclude that $s\parallel t$.

Step2: Identify alternate - interior angles

Alternate - interior angles are equal when lines are parallel. For $\angle2\cong\angle3$, since $\angle2$ and $\angle3$ are alternate - interior angles, by the Alternate Interior Angles Theorem, we can conclude that $d\parallel e$.

Step3: Identify alternate - exterior angles

Alternate - exterior angles are equal when lines are parallel. For $\angle6\cong\angle7$, since $\angle6$ and $\angle7$ are alternate - exterior angles, by the Alternate Exterior Angles Theorem, we can conclude that $s\parallel t$.

Step4: Identify same - side interior angles

Same - side interior angles are supplementary when lines are parallel. For $m\angle5 + m\angle8=180^{\circ}$, since $\angle5$ and $\angle8$ are same - side interior angles, by the Same - Side Interior Angles Postulate, we can conclude that $d\parallel e$.

Answer:

1. Lines $s$ and $t$ are parallel by the Corresponding Angles Postulate.
2. Lines $d$ and $e$ are parallel by the Alternate Interior Angles Theorem.
3. Lines $s$ and $t$ are parallel by the Alternate Exterior Angles Theorem.
4. Lines $d$ and $e$ are parallel by the Same - Side Interior Angles Postulate.