Lesson 2-2 Properties from Algebra (page 37) Essential Question Can you justify the conclusion of a conditional statement?

Properties from Algebra “What are you bringing to the table?” Do you remember your properties from algebra? You must keep your properties, definitions, postulates, and theorems in your “bag of tricks.”

If a = b and c = d, then a + c = b + d Properties of Equality (=) Addition Property: Subtraction Property: Multiplication Property: Division Property: Substitution Property: If a = b and c = d, then a - c = b - d If a = b, then ca = cb If a = b and c ≠ 0, then a / c = b / c If a = b, then either a or b may be substituted for the other in any equation or inequality.

a = a … Properties of Equality (=) Reflexive Property: Symmetric Property: Transitive Property: Distributive Property: If a = b, then b = a If a = b and b = c, then a = c a (b + c) = ab + ac

Properties of Congruence ( ≅ ) Reflexive Property: Symmetric Property: Transitive Property:

If AB = CD and BC = BC, then AB + BC = CD + BC. Statement a. Addition Property of Equality Justification

If 2 + YZ = 8, then YZ = 6. Statement b. Subtraction Property of Equality Justification

If 2 m ∠ 1=72º, then m ∠ 1=36º. Statement c. Division Property of Equality Justification

If Pt. B is between A and C, then AB + BC = AC. Statement d. Segment Addition Postulate Justification

If m ∠ A = m ∠ X & m ∠ X = m ∠ B, then m ∠ A = m ∠ B. Statement e. Transitive Property of Equality Justification

Statement f. Transitive Property of Congruence Justification

Statement g. Symmetric Property of Congruence Justification

Statement h. Definition of Right Angle or Def. Rt. ∠ Justification

Solve for “x” and supply reasons for each step. StepsReasons 1. 5 ( 3 x - 4 ) = 5 x _____________________________________________

Solve for “x” and supply reasons for each step. StepsReasons 1. 5 ( 3 x - 4 ) = 5 x _____________________________________________ x - 20 = 5 x _____________________________________________

Solve for “x” and supply reasons for each step. StepsReasons 1. 5 ( 3 x - 4 ) = 5 x _____________________________________________ x - 20 = 5 x _____________________________________________ x - 20 = 0 _____________________________________________

Solve for “x” and supply reasons for each step. StepsReasons 1. 5 ( 3 x - 4 ) = 5 x _____________________________________________ x - 20 = 5 x _____________________________________________ x - 20 = 0 _____________________________________________ x = 20 _____________________________________________

Solve for “x” and supply reasons for each step. Given Problem Distributive Property StepsReasons 1. 5 ( 3 x - 4 ) = 5 x _____________________________________________ x - 20 = 5 x _____________________________________________ x - 20 = 0 _____________________________________________ x = 20 _____________________________________________ 5. x = 2 _____________________________________________ Subtraction Prop. of = Addition Prop. of = Division Prop. of =

Complete the proof. Given: m ∠ 1 = m ∠ 3 Prove: m ∠ ABE = m ∠ DBC m ∠ 1 = m ∠ 3 Reflexive Property of = StatementsReasons 1.___________________Given 2.___________________ ___________________ 3.___________________ ___________________ 4.m ∠ ABE = _____________ ___________________ m ∠ DBC = _____________ 5.___________________ ___________________ Addition Prop. of = Angle Addition Post. Substitution Prop. ABC D E 13 2 m ∠ ABE = m ∠ DBC m ∠ 2 = m ∠ 2 m ∠ 1 + m ∠ 2 = m ∠ 3 + m ∠ 2 m ∠ 1 + m ∠ 2 m ∠ 3 + m ∠ 2

Complete the proof. Given: KP = ST ; PR = TV Prove: KR = SV KP = ST ; PR = TV StatementsReasons 1.___________________Given 2.___________________ ___________________ 3.KP + PR = _____________ ___________________ ST + TV = _____________ 4.___________________ ___________________ Addition Prop. of = Segment Add. Post. Substitution Prop. KPR KR = SV KP + PR = ST + TV KR SV STV

Assignment Written Exercises on pages 41 & 42 GRADED: 1 to 9 odd numbers Be sure to write out the entire proof! Can you justify the conclusion of a conditional statement?