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Lesson 2-6 Algebraic Proofs

Lesson 2-6 Algebraic Proofs. Using a group of algebraic steps to solve problems is a deductive argument A two-column proof contains statements and reasons organized in two columns. Solve. Example 6-1a. Algebraic Steps Properties. Original equation. Distributive Property.

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Lesson 2-6 Algebraic Proofs

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  1. Lesson 2-6 Algebraic Proofs • Using a group of algebraic steps to solve problems is a deductive argument • A two-column proof contains statements and reasons organized in two columns.

  2. Solve Example 6-1a Algebraic Steps Properties Original equation Distributive Property Substitution Property Addition Property

  3. Answer: Example 6-1b Substitution Property Division Property Substitution Property

  4. Solve Example 6-1c Algebraic Steps Properties Original equation Distributive Property Substitution Property Subtraction Property

  5. Answer: Example 6-1d Substitution Property Division Property Substitution Property

  6. 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 Example 6-2a

  7. Write a two-column proof for the following. a. Example 6-2f

  8. Proof: Statements Reasons 1. Given 1. 2. Multiplication Property 2. 3. Substitution 3. 4. Subtraction Property 4. 5. Substitution 5. 6. Division Property 6. 7. Substitution 7. Example 6-2g

  9. 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 Example 6-3a Read the Test Item Determine whether the statements are true based on the given information.

  10. Statement I:Examine the given information, GHJKST and . From the definition of congruence of segments, if , then STRP. You can substitute RP for ST in GHJKST to get GHJK RP. Thus, Statement I is true. Statement II:Since the order you name the endpoints of a segment is not important, and TS = PR. Thus, Statement II is true. Example 6-3b Solve the Test Item

  11. Statement IIIIf GHJKST, then . Statement III is not true. Example 6-3c Because Statements I and II only are true, choice B is correct. 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 Example 6-3d Answer: C

  13. Given: m leg 1 22 cm Prove: m leg 3 22 cm Example 6-4a SEA LIFE A 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. Proof: Statements Reasons 1. 1. Given 2. 2. Transitive Property 3. m leg 1 m leg 3 3. Definition of congruence 4. m leg 1 22 cm 4. Given 5. m leg 3 22 cm 5. Transitive Property Example 6-4a

  15. DRIVING A stop sign as shown below is a regular octagon. If the measure of angle A is 135 and angle A is congruent to angle G, prove that the measure of angle G is 135. Example 6-4b

  16. Proof: Statements Reasons 1. Given 1. 2. Given 2. 3. Definition of congruent angles 3. 4. Transitive Property 4. Example 6-4c

  17. p. P. 97 14-31, 37-38 (20 problems)

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