1. SWBAT use algebra to write two column proofs

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Presentation transcript:

1. SWBAT use algebra to write two column proofs Objectives: 1. SWBAT use algebra to write two column proofs 2. SWBAT use properties of equality to write geometric proofs Splash Screen

Preparation for G.CO.9 Prove theorems about lines and angles. Content Standards Preparation for G.CO.9 Prove theorems about lines and angles. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. CCSS

Use algebra to write two-column proofs. You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties of equality to write geometric proofs. Then/Now

algebraic proof two-column proof formal proof Vocabulary

Properties of Real Numbers: properties are true for any real numbers a, b, and c

Justify Each Step When Solving an Equation Solve 2(5 – 3a) – 4(a + 7) = 92. Algebraic Steps Properties 2(5 – 3a) – 4(a + 7) = 92 Original equation 10 – 6a – 4a – 28 = 92 Distributive Property –18 – 10a = 92 Substitution Property –18 – 10a + 18 = 92 + 18 Addition Property –10a = 110 Substitution Property Division Property a = –11 Substitution Property Example 1

Solve –3(a + 3) + 5(3 – a) = –50. A. a = 12 B. a = –37 C. a = –7 D. a = 7 Example 1

Begin by stating what is given and what you are to prove. Write an Algebraic Proof Begin by stating what is given and what you are to prove. Example 2

2. Addition Property of Equality Write an Algebraic Proof Statements Reasons Proof: 1. Given 1. d = 20t + 5 2. d – 5 = 20t 2. Addition Property of Equality 3. 3. Division Property of Equality = t 4. 4. Symmetric Property of Equality Example 2

Which of the following statements would complete the proof of this conjecture? If the formula for the area of a trapezoid is , then the height h of the trapezoid is given by . Example 2

3. Division Property of Equality Statements Reasons Proof: 3. 3. Division Property of Equality 4. 4. Symmetric Property of Equality 1. Given 1. 2. _____________ 2. Multiplication Property of Equality ? Example 2

A. 2A = (b1 + b2)h B. C. D. Example 2

Write a Geometric Proof Example 3

Proof: Statements Reasons 1. Given 2. Definition of ≅ angles 3. Transitive Property of Equity 4. Substitution 5. Substitution

Example 3

3. Definition of congruent segments Statements Reasons Proof: 1. Given 1. 2. 2. _______________ ? 3. AB = RS 3. Definition of congruent segments 4. AB = 12 4. Given 5. RS = 12 5. Substitution Example 3

A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3

HOMEWORK Page 139 #’s 9-20