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Geometry Chapter 2 Lesson 2-6 Example 1 Verify Algebraic Relationships Solve 4(x + 3) = 52. Algebraic Steps 4(x + 3) = 52 4x + 12 = 52 4x + 12 - 12 = 52 - 12 4x = 40 4x 40 = 4 4 x = 10 Properties Original Equation Distributive Property Subtraction property Substitution Property Division Property Substitution Property Example 2 Write a Two-Column Proof Write a two-column proof. a. If 2(3x + 4) = 56, then x = 8 Statements 1. 2(3x + 4) = 56 2. 2(3x) + 2(4) = 56 3. 6x + 8 = 56 4. 6x + 8 – 8 = 56 – 8 5. 6x = 48 6. 6x 48 = 6 6 7. x = 8 Reasons 1. Given 2. Distributive Property 3. Substitution 4. Subtraction Property 5. Substitution 6. Division Property 7. Substitution Geometry Chapter 2 Example 3 Justify Geometric Relationships Standardized Test Practice If A B, and B C, then which of the following is a valid conclusion? I II III mA = mB and mB = mC A C A is complementary to C A II only C I, II and III B I and II D I and III Read the Test Item Determine whether the statements are true based on the given information. Solve the Test Item Statement I: Examine the given information, A B, and B C. From the definition of congruent angles, if A B, and B C, then mA = mB and mB = mC. Thus, Statement I is true. Statement II: By the Transitive Property A C. Thus, Statement II is true. Statement III: There is no information about the sum of the measures of the angles so there is no way to determine if they are complementary. Thus, Statement III is not a valid conclusion. Because Statements I and II are true, choice B is correct. Example 4 Geometric Proof TIME On a clock, the angle formed by the hands at 4:00 is a 120° angle. If the angle formed at 4:00 is congruent to the angle formed at 8:00, prove that the angle formed at 8:00 is a 120° angle. Given: m 4 = 120 4 8 Prove: m8 = 120 Proof: Statements 1. m 4 = 120 4 8 2. m4 = m8 3. 120 = m8 4. m8 = 120 Reasons 1. Given 2. Definition of congruent angles 3. Substitution 4. Symmetric Property