CHAPTER 2: DEDUCTIVE REASONING

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

2. 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.

3. 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.

4. 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.

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

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

7. 3y + 4 = 2y/5 15y + 20 = 2y 13y + 20 = 0 13y = -20 y = -20/13 Given Mult. Prop. of = Subtr. Prop. of = Subtr. Prop. of = Div. Prop. of = PRACTICEJustify each step in solving the equation3y + 4 = 2y/5

8. 2x + 3 = 11 2x = 8 x = 4 Given Subtraction Property of Equality Division Property of Equality PRACTICEJustify each step in solving 2x + 3 = 11

9. ¾ x = 6 + 2x 3x = 24 + 8x -5x = 24 x = - 24/5 Given Mult. Prop. of = Subtr. Prop. of = Div. Prop. of = YOU TRYJustify each step in solving ¾ x = 6 + 2x

10. 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 = COMPLETING A 2-COLUMN PROOF G C Given: m 1 = m 3; m 2 = m 4 Prove: m ABC = m DEF H F 2 1 4 3 A B E D

11. 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 = 2 COLUMN PROOF Given: DW = ON Prove: DO = WN D O W N

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