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
(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 ⊥
∠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: