More Angle Relationships. Deductive Reasoning To deduce means to reason from known facts When you prove a theorem, you are using deductive reasoning using.

Presentation on theme: "More Angle Relationships. Deductive Reasoning To deduce means to reason from known facts When you prove a theorem, you are using deductive reasoning using."— Presentation transcript:

More Angle Relationships

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

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

Proof of Congruent Supplements Theorem

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

Congruent Supplements Theorem

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

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

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

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

Identifying Special Pairs of Angles Vertical Angles Are congruent

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

Download ppt "More Angle Relationships. Deductive Reasoning To deduce means to reason from known facts When you prove a theorem, you are using deductive reasoning using."

Similar presentations