Warm Up 10.03.11 Week 8 If it does not snow, then we will go camping. If we go camping then we will cook marshmallows. The following statement depicts.

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Presentation transcript:

Warm Up Week 8 If it does not snow, then we will go camping. If we go camping then we will cook marshmallows. The following statement depicts which law of deductive reasoning?

Geometry 2.6 Day 1 I will understand and use angle congruence properties to prove statements. Properties of Angle Congruence Reflexive ∠ A ≅ ∠ A Symmetric IF ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A Transitive IF ∠ A ≅ ∠ B, and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C Theorem 2.2

StepReason Ex 1 Given Definition of congruent angles Given Given: Prove: ∠ A ≅ ∠ C ∠ B ≅ ∠ C m ∠ A = m ∠ B ∠ A ≅ ∠ B Given: ∠ B ≅ ∠ C A B C ∠ A ≅ ∠ B Definition of congruent angles m ∠ B = m ∠ C m ∠ A = m ∠ C Substitution property of equality ∠ A ≅ ∠ C Definition of congruent angles

∠ 2 ≅ ∠ 3 StepReason Ex 2 m ∠ 3 = 40⁰ Given ∠ 1 ≅ ∠ 2 Given ∠ 2 ≅ ∠ 3 Given Transitive property of Equality Given: Prove: m ∠ 1 = 40⁰ ∠ 1 ≅ ∠ 3 m ∠ 1 = m ∠ 3 Definition of congruent angles Substitution property of equality m ∠ 3 = 40⁰ ∠ 1 ≅ ∠ 2 Given: m ∠ 1 = 40⁰

∠ 2 ≅ ∠ 3 StepReason Ex 2 m ∠ 3 = 40⁰ Given ∠ 1 ≅ ∠ 2 Given ∠ 2 ≅ ∠ 3 Given Transitive property of Equality Given: Prove: m ∠ 1 = 40⁰ ∠ 1 ≅ ∠ 3 m ∠ 1 = m ∠ 3 Definition of congruent angles Substitution property of equality m ∠ 3 = 40⁰ ∠ 1 ≅ ∠ 2 Given: m ∠ 1 = 40⁰

Theorem 2.3 Right Angle Congruence All right angles are congruent. A B

StepReason ∠ 1 and ∠ 2 are right angles Given Definition of right angles m ∠ 1 = 90⁰ m ∠ 2 = 90⁰ m ∠ 1 = m ∠ 2 Substitution property of equality ∠ 1 ≅ ∠ 2 Definition of congruent angles Given: Prove: ∠ 1 ≅ ∠ 2 ∠ 1 and ∠ 2 are right angles Ex 3 A B Definition of right angles

All right angles are ______________. Review Assignment: Do 1: Textbook Page 113, 10 – 17 all and Page 125, 40 – 50 evens ∠ 3 ≅ ∠ 4 Given: Prove: m ∠ 4 = 25⁰ m ∠ 2 = 25⁰ ∠ 2 ≅ ∠ 3 Given: