Question

problem 22
given: $overline{mn}paralleloverline{pq}paralleloverline{sr}$, $overline{mr}paralleloverline{st}$
prove: $angle1congangle2$

1. click here to insert
2. given
3. $angle1congangle prs$
4. click here to insert
5. $angle prscongangle2$
6. click here to insert

Explanation:

Step1: State given information

$\overline{MN}\parallel\overline{PQ}\parallel\overline{SR}$, $\overline{MR}\parallel\overline{ST}$

Step2: Use corresponding - angles postulate for $\angle1$ and $\angle PRS$

Since $\overline{MN}\parallel\overline{SR}$, $\angle1\cong\angle PRS$

Step3: Use corresponding - angles postulate for $\angle PRS$ and $\angle2$

Since $\overline{MR}\parallel\overline{ST}$, $\angle PRS\cong\angle2$

Step4: Apply transitive property of congruence

If $\angle1\cong\angle PRS$ and $\angle PRS\cong\angle2$, then $\angle1\cong\angle2$

Answer:

1. $\overline{MN}\parallel\overline{PQ}\parallel\overline{SR}$, $\overline{MR}\parallel\overline{ST}$
2. Corresponding - angles postulate (Since $\overline{MN}\parallel\overline{SR}$, $\angle1$ and $\angle PRS$ are corresponding angles)
3. Corresponding - angles postulate (Since $\overline{MR}\parallel\overline{ST}$, $\angle PRS$ and $\angle2$ are corresponding angles)
4. $\angle1\cong\angle2$ (By the transitive property of congruence, because $\angle1\cong\angle PRS$ and $\angle PRS\cong\angle2$)