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
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: AB


n: CD

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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