Question

4.) given: g || h and ∠1 ≅ ∠2 prove: p || r statements reasons 1.) g || h 2.) def of correspond ∠s 3.) ∠1 ≅ ∠3 given 4.) alternate ext ∠s thm 5.) 6.) ∠3 and ∠2 are alt ext ∠s 7.)

Explanation:

Step1: State given fact

Given

Step2: Since g || h, find corresponding angles

$\angle1\cong\angle3$ (by definition of corresponding angles when g || h)

Step3: State given angle - congruence

$\angle1\cong\angle2$ (given)

Step4: Transitive property of congruence

$\angle2\cong\angle3$ (since $\angle1\cong\angle3$ and $\angle1\cong\angle2$)

Step5: Identify alternate - exterior angles

$\angle3$ and $\angle2$ are alternate - exterior angles

Step6: Apply alternate - exterior angles theorem

If alternate - exterior angles are congruent, then the lines are parallel. So, $p\parallel r$

Answer:

1. Given
2. $\angle1\cong\angle3$
3. Given
4. $\angle2\cong\angle3$ (Transitive property of congruence)
5. Definition of alternate - exterior angles
6. Given
7. $p\parallel r$ (Alternate Exterior $\angle$'s Thm)