UNIT 2 Algebraic Proofs 2.5 A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. An important part of writing a proof is giving justifications to show that every step is valid.

Solve for x given 3(x -1) – 3 = 11. UNIT 2 Algebraic Proofs 2.5 Solve for x given 3(x -1) – 3 = 11. Justify each step!

Properties of Equality see page 104 UNIT 2 Algebraic Proofs 2.5 Properties of Equality see page 104 Addition Property………If a=b, then a+c = b+c Subtraction Property…..If a=b, then a–c = b–c Multiplication Property...If a=b, then a•c = b•c Division Property……....If a=b and c0, then ac = bc Reflexive Property……..a = a Symmetric Property……If a = b, then b = a Transitive Property…….If a = b and b = c, then a = c Substitution Property….If a=b, then b can replace a in any expression. Distributive Property…..a(b + c) = a•b + a•c not on 104

Properties of Congruence see page 106 UNIT 2 Algebraic Proofs 2.5 Earlier we said geometric figures, like segment and angles are congruent instead of equal (XY  WV). Since numbers are different than figures, we must have some properties of congruence for those figures. Properties of Congruence see page 106 Reflexive Property of Congruence……EF  EF Symmetric Property of Congruence….if 12 then 21 Transitive Property of Congruence…...if AB  CD and CD  EF, then AB  EF

Name the property illustrated in each statement UNIT 2 Algebraic Proofs 2.5 Name the property illustrated in each statement a. If x = y and y + 4 = 3x, then x + 4 = 3x. The property is the Substitution Prop. of Equality. b. If x + 4 = 3x, then 4 = 2x. The property is the Subtraction Prop. of Equality. c. If P Q, Q R, and R S, then P S. Transitive Property of Congruence. d. If ST UV then UV ST Symmetric Property of Congruence.

UNIT 2 Algebraic Proofs 2.5 Review properties on page 104 and 106. Then name the property that justifies each statement. If AB = CD, then AB + XY = CD + XY If XD = FY and FY = 12, then XD = 12 If XY + JM = GT + XY, then JM = GT If 2(mABC) = 180, then mABC = 90 RS = RS If mABC = 25, then 25 = mABC Use the given property to complete each statement. Symmetric Prop of Eq. If MN = UT, then ________ Div. Prop of Eq. If 4mQWR= 120, then ________ Transitive Prop of Eq. If SB=VT and VT=MN, then _______ Add. Prop of Eq. If y-15 = 36, then y-10 = _________ Reflexive Prop of Eq. JL ≌ _________ Substitution Prop of Eq. If 2x+3a=7 and 3a=2, then________

UNIT 2 Algebraic Proofs 2.5 Solve for x and write a justification for each step. NO = NM + MO Segment Addition Post. 4x – 4 = 2x + (3x – 9) Substitution Property of Equality 4x – 4 = 5x – 9 Simplify. –4 = x – 9 Subtraction Property of Equality 5 = x Addition Property of Equality

UNIT 2 Algebraic Proofs 2.5 Solve for x and write a justification for each step. ABD + DBC = ABC AAP (3x + 5) + (6x – 16) = 8x Subst 9x - 11= 8x Simplify x - 11= 0 SPE x = 11 APE

Homework: 2.5(107): 16,21,23,25-28,34