1. More Angle Relationships

2. Deductive Reasoning To deduce means to reason from known facts When you prove a theorem, you are using deductive reasoning using the existing structure to deduce new parts of the structure In geometry, as in construction, new parts of the structure are built upon existing parts

3. Congruent Supplements Theorem If ∠1 and ∠2 are supplementary and ∠3 and ∠4 are supplementary and ∠2 ∠4 Then ∠1 ∠3

4. Proof of Congruent Supplements Theorem

5. Congruent Supplements Theorem If ∠1 and ∠2 are supplementary and ∠2 and ∠3 are supplementary Then ∠1 ∠3

6. Congruent Supplements Theorem

7. Congruent Complements Theorem If ∠1 and ∠2 are complementary and ∠3 and ∠4 are complementary and ∠2 ∠4 Then ∠1 ∠3

8. Congruent Complements Theorem Given: ∠1 and ∠2 are complementary ∠3 and ∠4 are complementary ∠2 ∠4 Prove: ∠1 ∠3 m ∠1+m∠2=90° Definition of complementary m ∠3+m∠4=90° Definition of complementary m ∠1+m∠2= m ∠3+m∠4 Transitive prop ∠2 ∠4Given m ∠2=m∠4Definition of congruent m ∠1+m∠2= m ∠3+m∠2Substitution m ∠1=m∠3Subtraction prop ∠1 ∠3 Definition of congruent

9. Congruent Complements Theorem If ∠4 and ∠5 are complementary and ∠5 and ∠6 are complementary Then ∠4 ∠6

10. Proof of Congruent Complements Theorem Fill in the missing steps and missing reasons

11. Identifying Special Pairs of Angles Vertical Angles Are congruent

12. Vertical Angles Theorem If two angles are vertical angles, then they are congruent. Statements Reasons Given Def of linear pair Congruent supplements Theorem Def of congruent angles