University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2019
Views:

270

Pages:

2
Author:

StellarSymphony

Reteach A/gebraic Proof А proof is а logical argument that shows а conclusion is true. An algebraic proof uses algebraic properties, including the Distributive Property and the properties of equality. Examples Symbols Properties of Equality Addition lf а = Ь, then а+ с= Ь + с. lf х = -4, then х + 4 = -4 + 4. SuЬtraction lf а = Ь, then а - с= Ь - с. lf r+ 1 = 7, then r+ 1 -1 = 7 -1. Multiplication lf а = Ь, then ас= Ьс. lf ':.. = 8, then ':.. (2) = 8(2). Division а Ь lf а = 2 and с* О, then -=-. lf 6 =31, then Reflexive а=а 15 = 15 Symmetric lf а= Ь, then Ь = а. lf п = 2, then 2 = п. Transitive lf а = Ь and Ь = с, then а = с. lf у= 3 and 3 = 9, then у= 9. Substitution lf а = Ь, then Ь сап Ье substituted for а in any expression. lf х = 7, then 2х =2(7). 2 с с 2 2 6 31 3 = 3. 2 When solving an algebraic equation, justify each step Ьу using а definition, property, or piece of given information. 2(а+1)=-6 Given equation 2а+2 =-6 -2 -2 Distributive Property SuЬtraction Property of Equality 2а=-8 -8 2а = 2 2 Simplify. а=-4 Simplify. Division Property of Equality Reteach A/gebraic Proof continued When writing algebraic proofs in geometry, you сап also use definitions, postulates, properties, and pieces of given information to justify the steps. mLJKM = mLMKL 0 0 Definition of congruent angles (5х - 12) = 4х Substitution Property of Equality х-12=0 Х= 12 SuЬtraction Property of Equality Properties of Congruence Reflexive Symmetric Transitive J 4х" к---- L Addition Property of Equality Examples Symbols = figure А lf figure А = figure В, then figure В= figure А. lf figure А = figure В and figure В= figure С, then figure А = figure С. figure А м (SX - 12)0 LCDE:LCDE = - - lf JK - LM, then LM = JK. lf LN:LPand LP:LQ, then LN:LQ.