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