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Given: m is perpendicular to L and n to L,prove: m is parallel to n

write a two column proof of theorem 3.12

given m is perpendicular to L and N to L.

Prove: M is parallel to N

^
|B      A
<-------------------|-------.--------> m
|
|
.C
|
<-------------------|-------.--------> n
|D       E
|
| L

Statement                                                                    Reason
line m is perpendicular to line L                                      Given
line n is perpendicular to line L                                       Given
line m makes right angle (angle ABC) to line L                 Definition of perpendicular lines
line n makes right angle (angle CDE) to line L                  Definition of perpendicular lines
angle ABC = 90° and angle CDE = 90°                            Definition of right angle
angle ABC + angle CDE = 180°                                       Addition property of equality
line m is parallel to line n                                               Converse of same side interior angles theoram (if same side interior angles are supplementary, then the lines are parallel)

Using the following diagram with points A,B,C,D marked

L:  |

m:     A-------------------B---------------------------

|

|

n:     ---------------------C--------------------------D

|

Statement                                |    Reason

m and n perpendicular to L        |    Given.

ABC and DCB are right angles    |    Definition of perpendicular.

ABC = DCB = 90°                     |    Definition of right angle.

m || n                                     |     Alternate interior angle theorem.

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