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Finish the two column proof given below to show that p ll q by filling in the...

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novjb | Salutatorian

Posted June 28, 2013 at 1:05 AM via web

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Finish the two column proof given below to show that p ll q by filling in the blanks. 

Statements              Reasons

1.r ll s                      1. Given

2. <2 `cong` <3              2. _____

3.<1 `cong` <3               3. _____

4._______               4.______

5. p ll q                     5.______

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2 Answers | Add Yours

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 28, 2013 at 1:37 AM (Answer #1)

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The lines r and s are parallel. As p is a transversal the alternate interior angles` /_1` and` /_3` are equal.

`/_2 = /_3` : Given

 

`/_1 = /_3` : alternate interior angles

`/_2 = /_1` : As `/_2 = /_3` and  `/_1 = /_3`

p ||q : As the corresponding angles `/_2` and `/_1` are equal.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 28, 2013 at 2:13 AM (Answer #2)

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1. `r || s`           1. Given

2. `/_2 cong /_3` 2. Given (marked in diagram)

3. `/_1 cong /_3` 3. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

4. `/_1 cong /_2` 4. The transitive property of congruence (or substitution.)

5. `p || q`          5. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

 

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