Question

3.) given: a||b
prove: ∠1 and ∠8 are supplementary
4.) given: g||h and ∠1≅∠2
prove: p||r

statements reasons
1.) given
2.) corresponding ∠s thm
3.) definition of ≅ ∠s
4.) definition of linear pair thm
5.) definition of supp ∠s
6.) substitution property of =
7.) definition of supp ∠s

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

Explanation:

3.

Step1: State the given

$a\parallel b$

Step2: Use corresponding - angles theorem

$\angle1\cong\angle5$ (Corresponding $\angle$'s Thm)

Step3: Define congruent angles

$m\angle1 = m\angle5$ (Definition of $\cong\angle$'s)

Step4: Recall linear - pair theorem

$\angle5$ and $\angle8$ are a linear pair, so $m\angle5 + m\angle8=180^{\circ}$ (Definition of Linear Pair Thm)

Step5: Define supplementary angles

If the sum of the measures of two angles is $180^{\circ}$, they are supplementary.

Step6: Substitute

Since $m\angle1 = m\angle5$, then $m\angle1 + m\angle8=180^{\circ}$ (Substitution Property of =)

Step7: Define supplementary angles again

$\angle1$ and $\angle8$ are supplementary (Definition of supp $\angle$'s)

Step1: State the given

$g\parallel h$

Step2: Use the definition of corresponding angles

$\angle1$ and $\angle3$ are corresponding angles, so $\angle1\cong\angle3$ (Def of Correspond $\angle$'s)

Step3: State the given congruence

$\angle1\cong\angle2$ (Given)

Step4: Given information restated

(Already stated in step 3)

Step5: Use the alternate - exterior angles theorem

If $\angle2\cong\angle3$, then $p\parallel r$ (Alternate Ext $\angle$'s Thm)

Step6: Identify alternate - exterior angles

$\angle3$ and $\angle2$ are alt ext $\angle$'s

Step7: Conclude parallel lines

$p\parallel r$

Answer:

The statements and reasons to prove that $\angle1$ and $\angle8$ are supplementary are completed as above.

4.