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Axioms of Equality
Common Core Geometry Homework

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

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