5. The proof to show that AC = EC is as follows
Statements    Â
                      Reason
(1) AB = ED and C is the midpoint of
Â
  Given
(2) BC = DC Â Â Â Â Â
                      Definition of midpoint C of ![\overline {BD}](/tpl/images/0898/2800/33115.png)
(3) AB + BC = ED + CD Â Â Â
              Addition property of equality
(4) AC = EC Â Â Â Â
                      Substitution Property
6. The paragraph proof to show ∠2 and ∠3 are supplementary is as follows;
Statements    Â
                      Reason
m∠1 = m∠3    Â
   because they are alternate interior angles
m∠1 + m∠2 = 180° Â
because they are the sum of angles on a straight line
m∠3 + m∠2 = 180° Â
 due to the transitive property axiom
∠2 and ∠3 are supplementary Â
 because they add up to 180°
7. The two column proof is as follows;
Statements    Â
                      Reason
,
⊥
  Â
      given
m∠1 = m∠2   Â
          given
∠DBA = ∠DBC = 90° Â
    definition of
⊥ ![\overline {AC}](/tpl/images/0898/2800/d8b2c.png)
∠DBA = m∠1 + m∠3  Â
     angle addition postulate
∠DBC = m∠2 + m∠4  Â
    angle addition postulate   Â
m∠1 + m∠3 = m∠2 + m∠4 Â
 transitive property
m∠3 = m∠4   Â
          addition property of equality
Step-by-step explanation: