CHAPTER 2: DEDUCTIVE REASONING Section 2-2: PROPERTIES FROM ALGEBRA

PROPERTIES OF EQUALITY Addition Property: If a = b and c = d, then a + c = b + d Subtraction Property: If a = b and c = d, then a – c = b – d 3. Multiplication Property: If a = b, then ca = cb.

PROPERTIES OF EQUALITY Division Property If a = b and c ≠ 0, then a/c = b/c Substitution Property If a = b, then either a or b may be substituted for the other in any equation or inequality.

PROPERTIES OF EQUALITY Reflexive Property a = a Symmetric Property If a = b, then b = a Transitive Property If a = b and b = c, then a = c.

PROPERTIES OF CONGRUENCE Reflexive Property DE ≡ DE D ≡ D Symmetric Property If DE ≡ FG, then FG ≡ DE If D ≡ E, then E ≡ D.

PROPERTIES OF CONGRUENCE Transitive Property If DE ≡ FG and FG ≡ JK, then DE ≡ JK. If D ≡ E and E ≡ F, then D ≡ F.

PRACTICE Justify each step in solving the equation 3y + 4 = 2y/5 Given Mult. Prop. of = Subtr. Prop. of = Div. Prop. of = 3y + 4 = 2y/5 15y + 20 = 2y 13y + 20 = 0 13y = -20 y = -20/13

PRACTICE Justify each step in solving 2x + 3 = 11 Given Subtraction Property of Equality Division Property of Equality

YOU TRY Justify each step in solving ¾ x = 6 + 2x Given Mult. Prop. of = Subtr. Prop. of = Div. Prop. of =

COMPLETING A 2-COLUMN PROOF Given: m 1 = m 3; m 2 = m 4 Prove: m ABC = m DEF H F 2 1 4 3 A B E D m 1 = m 3; m 2 = m 4 m 1 + m 2 = m 3 + m 4 m 1 + m 2 = m ABC m 3 + m 4 = m DEF 4. m ABC = m DEF Given Add. Prop. of = Angle Add. Post. Substitution Prop. of =

2 COLUMN PROOF DW = ON DW = DO + OW; ON = OW + WN 3.DO + OW = OW +WN Given: DW = ON Prove: DO = WN D O W N DW = ON DW = DO + OW; ON = OW + WN 3.DO + OW = OW +WN 4. OW = OW 5. DO = WN Given Segment Add. Post. Substitution Prop. Reflexive Prop. Subtr. Prop. of =

HOMEWORK Classwork Pg. 40, Classroom Exercises 1-12 ALL Pg. 41-42, Written Exercises 2-10 Even