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Lesson 2-6

Lesson 2-6. Algebraic Proof. Transparency 2-6. 5-Minute Check on Lesson 2-5. In the figure shown, A, C, and DH lie in plane R , and B is on AC . State the postulate that can be used to show each statement is true. 1. A, B, and C are collinear. 2. AC lies in plane R .

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Lesson 2-6

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  1. Lesson 2-6 Algebraic Proof

  2. Transparency 2-6 5-Minute Check on Lesson 2-5 In the figure shown, A, C, and DH lie in plane R, and B is on AC. State the postulate that can be used to show each statement is true. 1. A,B, and C are collinear. 2. AC lies in plane R . 3. A, H, and D are coplanar. 4. E and F are collinear. 5. DH intersects EF at point B. 6. Which statement is not supported by a postulate? Standardized Test Practice: A R and S are collinear. M lies on LM. B C P, X and Y must be collinear. D J, K and L are coplanar.

  3. Transparency 2-6 5-Minute Check on Lesson 2-5 In the figure shown, A, C, and DH lie in plane R , and B is on AC. State the postulate that can be used to show each statement is true. 1. A,B, and C are collinear. A line contains at least two points. 2. AC lies in plane R . If two points lie in a plane, then the entire line containing those points lies in that plane. 3. A, H, and D are coplanar. Through any 3 points not on the same line, there is exactly one plane. 4. E and F are collinear. Through any 2 points, there is exactly one line. 5. DH intersects EF at point B. If two lines intersect, then their intersection is exactly one point. 6. Which statement is not supported by a postulate? Standardized Test Practice: A R and S are collinear. M lies on LM. B C P, X and Y must be collinear. D J, K and L are coplanar.

  4. Objectives • Use algebra to write two-column proofs • Use properties of equality in geometry proofs

  5. Vocabulary • Deductive argument– a group of logical steps used to solve problems • Two-column proof – also known as a formal proof

  6. Algebraic Properties

  7. Solve 2(5 – 3a) – 4(a + 7) = 92 Algebraic StepsProperties 2(5 – 3a) – 4(a + 7) = 92 Original equation 10 – 6a – 4a – 28 = 92 Distributive Property –18 – 10a = 92 Substitution Property –18 + 18 – 10a = 92 + 18 Addition Property –10a = 110 Substitution Property Division Property a = – 11 Substitution Property Answer: a = – 11

  8. If Write a two-column proof. then Proof: Statements Reasons 1. Given 1. 2. 2. Multiplication Property 3. 3. Substitution 4. 4. Subtraction Property 5. 5. Substitution 6. 6. Division Property 7. 7. Substitution

  9. Proof: Statements Reasons a. 1. Given 1. 2. Multiplication Property 2. 3. Substitution 3. 4. Subtraction Property 4. 5. Substitution 5. 6. Division Property 6. 7. Substitution 7. Write a two-column proof.

  10. Proof: Statements Reasons 1. Given 1. 2. Multiplication Property 2. 3. Distributive Property 3. 4. Subtraction Property 4. 5. Substitution 5. 6. Subtraction Property 6. 7. Substitution 7. Write a two-column proof. b.Given: Prove: a = –5

  11. MULTIPLE-CHOICE TEST ITEM If and then which of the following is a valid conclusion? I II III A I only B I and II C I and III D I, II, and III Read the Test Item Determine whether the statements are true based on the given information. Answer: B

  12. MULTIPLE- CHOICE TEST ITEM If and then which of the following is a valid conclusion? I. II. III. A I only B I and II C I and III D II and III Answer: C

  13. Proof: Statements Reasons Given: 1. 1. Given m leg 1 22 cm 2. 2. Transitive Property 3. m leg 1 m leg 3 3. Definition of congruence Prove: m leg 3 22 cm 4. m leg 1 22 cm 4. Given 5. m leg 3 22 cm 5. Transitive Property SEA LIFEA starfish has five legs. If the length of leg 1 is 22 centimeters, and leg 1 is congruent to leg 2, and leg 2 is congruent to leg 3, prove that leg 3 has length 22 centimeters.

  14. Summary & Homework • Summary: • Algebraic properties of equality can be applied to the measures of segments and angles to prove statements • Homework: • pg 97-8: 4-9, 15-18, 24, 25

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