1 / 12

CHAPTER 2: DEDUCTIVE REASONING

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.

petula
Télécharger la présentation

CHAPTER 2: DEDUCTIVE REASONING

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related