Question

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

If $\angle1\cong\angle4$, by the Corresponding - Angles Postulate, if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. So, $s\parallel t$.

Step2: Identify alternate - interior angles

If $\angle2\cong\angle3$, by the Alternate - Interior Angles Theorem, if two lines are cut by a transversal and the alternate - interior angles are congruent, then the lines are parallel. So, $d\parallel a$.

Step3: Identify alternate - exterior angles

If $\angle6\cong\angle7$, by the Alternate - Exterior Angles Theorem, if two lines are cut by a transversal and the alternate - exterior angles are congruent, then the lines are parallel. So, $d\parallel a$.

Step4: Identify same - side interior angles

If $m\angle5 + m\angle8=180^{\circ}$, by the Same - Side Interior Angles Postulate, if two lines are cut by a transversal and the same - side interior angles are supplementary, then the lines are parallel. So, $d\parallel a$.

Answer:

1. $s\parallel t$ by the Corresponding - Angles Postulate.
2. $d\parallel a$ by the Alternate - Interior Angles Theorem.
3. $d\parallel a$ by the Alternate - Exterior Angles Theorem.
4. $d\parallel a$ by the Same - Side Interior Angles Postulate.