Algebraic Properties Copy the following on a clean sheet of paper PropertyDescription Reflexive PropertyFor every number a, a = a Symmetric PropertyFor.

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Presentation transcript:

Algebraic Properties Copy the following on a clean sheet of paper PropertyDescription Reflexive PropertyFor every number a, a = a Symmetric PropertyFor all numbers a and b, if a = b, b = a Transitive PropertyFor all numbers a, b, and c, if a=b and b=c then a=c Additive and Subtractive Property For all numbers, a, b, and c, if a = b then a + c = b + c and a – c = b - c Multiplicative and Division Properties For all numbers, a, b, and c if a = b then a*c = b*c and if c  0 a/c = b/c Substitution PropertyFor all numbers a and b if a = b, then a may be replace by b in any equation or expression Distributive PropertyFor all numbers a, b, and c a(b + c) = ab + ac Be true to your work, your word, and your friend. Henry David Thoreau

Geometric Properties PropertySegmentsAngles Reflexive Property AB = AB m  1 =m  1 Symmetric Property If AB = CD, then CD = AB If m  1= m  2, then m  2= m  1 Transitive Property If AB = CD, and CD = EF, then AB = EF If m  1 = m  2, m  2 = m  3, then m  1 = m  3

Chapter 2.6 Algebraic Proofs Check.2.3 Recognize and apply real number properties to vector operations and geometric proofs (e.g. reflexive, symmetric, transitive, addition, subtraction, multiplication, division, distributive, and substitution properties). CLE Develop an understanding of the tools of logic and proof, including aspects of formal logic as well as construction of proofs. Spi.1.4Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems Spi.4.4Analyze different types and formats of proofs Objective: Practice writing proofs for algebraic problems

Writing Proofs 1. a. If x then b, if b then a b. If y then z, If z then b, If b then a 2. a. If a then c; If b & c then e b. If f then b, if a then c, if b & c, then e; d if and only if e 3. a. If e then a, if a then b; if b & c then d b. If d then e, if e then a c. Cannot be proven 1. If purple then red, if red then blue 2. Cannot be proven 3. If blue then silver; if red and silver then black 4. If blue then silver, if pink then red, if red and silver then black

Algebraic Proof Formal/Two Column- process Statements Reasons 1. Given 2. Distributive Property 3. Substitution 4. Addition Property 5. Substitution 6. Division Property 7. Substitution

Algebraic Proof Formal/Two Column- process Statements Reasons 1. Given 2. Multiplicative Property 3. Substitution 4. Subtractive Property 5. Substitution 6. Division Property 7. Substitution

Write an Algebraic Proof Begin by stating what is given and what you are to prove.

Write an Algebraic Proof 2. d – 5 = 20t2. Addition Property of Equality StatementsReasons Proof: 1. Given 1. d = 20t Symmetric Property of Equality 3.3. Division Property of Equality = t

Example 3

StatementsReasons Proof: 1. Given _______________ ? 3. AB = RS3. Definition of congruent segments 4. AB = 124. Given 5. RS = 125. Substitution

Practice Assignment Page 137, Even