Given: m∠1 = m∠2

And points D,F, and E are colinear
       __   __  
Prove: AB ⊥ ED 

                                     
  






m∠1 = m∠2                                    Given

∠1 and ∠2 form a linear pair              D,F, and E are colinear
                                           and adjacent angles
                                           which form a straight
                                           line form a linear pair 

∠1 is supplementary to ∠2                 If two angles form a linear pair,
                                           they are supplementary


m∠1 + m∠2 = 180°                          Supplementary angles have sum 180°

m∠1 + m∠1 = 180°                          A quantity may be substituted
                                           for its equal

   2(m∠1) = 180°                          Definition of like terms 

      m∠1 = 90°                           Halves of equal quantities are
                                           equal

  ∠1 is a right angle                      Definition of a right angle is one
                                           whose measure is 90°
    __   __
    AB ⊥ ED                               Definition of perpendicular
                                           lines. 

Edwin