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

Question

 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

 

Answer 1

                         ^
                          |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)

Answer 2

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.