Warm Up 09.28.11 Week 7 1) What is the postulate? A B C D m∠ ADB + m ∠ BDC = m ∠ ADC 2) If ∠ 4 and ∠ 5 are a linear pair and ∠ 4 = 79⁰. What is m ∠ 5?

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Presentation transcript:

Warm Up Week 7 1) What is the postulate? A B C D m∠ ADB + m ∠ BDC = m ∠ ADC 2) If ∠ 4 and ∠ 5 are a linear pair and ∠ 4 = 79⁰. What is m ∠ 5?

Geometry 2.4 Day 1 I will use the properties of algebra to write reasons for steps in solving equations. Properties of Equality Addition: If a = b then a + c = b + c Subtraction: If a = b then a - c = b - c

Multiplication: Division: If a = b then ac = bc If a = b then cc = a b Properties of Equality

Substitution: Distributive: If a = b then b can replace a. If a( b + c ) = ab + ac Properties of Equality

Ex 1 55z – 3( 9z + 12 ) = -64 Solve and give reasons: StepReason 55z – 3( 9z + 12 ) = -64 Given 55z - 27z - 36 = -64Distributive property 28z - 36 = -64Simplify 28z = -28 Addition property of equality z = -1 Division property of equality

Properties of equality for Segment length Reflexive: Symmetric: AB = AB Transitive: If AB = CD, then CD = AB If AB = CD, and CD = EF, then AB = EF. Segment Length

Properties of equality for angle measure Reflexive: Symmetric: Transitive: m∠ A = m ∠ A If m∠ A = m ∠ B, then m ∠ B = m∠ A If m∠ A = m ∠ B, and m ∠ B = m∠ C then m∠ A = m∠ C Angle Measure

Ex 2 m ∠ 1 + m ∠ 2 = 132⁰ m ∠ 2 = 105⁰ 2 1 StepReason m ∠ 1 + m ∠ 2 = 132⁰ Given m ∠ 2 = 105⁰ Given show that m ∠ 1 = 27⁰

Ex 1 m ∠ 1 + m ∠ 2 = 132⁰ m ∠ 2 = 105⁰ 2 1 StepReason m ∠ 1 + m ∠ 2 = 132⁰ Given m ∠ 2 = 105⁰ Given show that m ∠ 1 = 27⁰

Ex 3 m ∠ 1 + m ∠ 2 = 132⁰ m ∠ 2 = 105⁰ 2 1 StepReason m ∠ 1 + m ∠ 2 = 132⁰ Given m ∠ 2 = 105⁰ Given m ∠ ⁰ = 132⁰ Substitution property of Eq. m ∠ 1 = 27⁰ Subtraction property of Eq. show that m ∠ 1 = 27⁰

Do: 1 5x + 7y = 58 Assignment: Textbook Page 99, All What is the property when 5x + 7y = 58 5( 27 ) + 7y = 58 ? given and x = 27