Algebra Proofs by ert554898


									  Algebra Proofs

By Dylan Keretz
   6th period
                    Memory Jogger
•   Let a, b, and c be all real numbers.
            / = Division
•   Addition Property                       If a=b, then a+c=b+c
•   Subtraction Property                     If a=b, then a-c=b-c
•   Multiplication Property                 If a=b, then ac=bc
•   Division Property                  If a=b and c=0, then a/c=b/c
•   Reflexive Property                 For any real number a, a=a
•   Symmetric Property                         If a=b, then b=a
•   Transitive Property                   If a=b and b=c, then a=c
•   Substitution Property            If a=b, then a can be substituted
                                  for b in any equation or expression
   Proving Statements About
• A true statement that          • Properties of Segment
  follows as a result of other     Congruence
  true statements is called a    • s=segment c=congruent to.
  theorem. All theorems must       Applies to all slides.
  be proved. You can prove a     • Reflexive For any
  theorem using a two-             segment AB, sAB c sAB
  column proof. A two-column     • Symmetric If sAB c sCD,
  proof has numbered               then sCD c sAB
  statements and reasons         • Transitive If sAB c sCD,
  that show the logical order      and sCD c sEF, then sAB
  of an argument.                  c sEF.
               Example 1
• Given: sPQ c sXY
• Prove: sXY c sPQ
  Statements             Reasons
1.sPQ c sXY          1. Given
2. PQ = XY           2. Def. of congruent segments
3. XY=PQ             3. Symmetric prop. Of equality
4. sXY c sPQ         4. Def. of congruent segments
•    Given: LK=5, JK=5, sJK
     c sJL
•    Prove: sLK c sJL                   3.   LK=JK
 Statements        Reasons                   LK=LJ
1. JK=5           1. Given
 2. LK=5             2. Given
3. ?              3. Transitive prop.
                    of equality
4. sLK c sJK    4. Def. of congruent
5.sJK c sJL      5. Given
6. sLK c sJL.    6.Transitive Prop.
                   Of Congruence
 Proving Statements
    About Angles

• Properties of Angle Congruence
• Angle congruence is reflexive, symmetric, and transitive.
      Here are some examples:
      NOTE: ^ = angle

• Reflexive                   For any angle A, ^A c ^A.
• Symmetric                    If ^A c ^B, then ^B c ^A.
• Transitive            If ^A c ^B and ^B c ^C, then ^A c ^C.
• Given: ^A c ^B       Prove: ^A c ^C
         ^B c ^C
      Statements           Reasons
   1. ^A c ^B,         1. Given
      ^B c ^C
   2. m^A = m^B        2. Def. of congruent angles
   3. m^B = m^C        3. Def. of congruent angles
   4. m^A = m^C        4. Transitive prop. Of equality
   5. ^A c ^C          5. Def. of congruent angles
•    Given: m^3=40 , ^1 c ^2, ^2 c ^3
•    Prove: m^1 = 40
  Statements                       Reasons
1.m^3 = 40 , ^1 c ^2, ^2 c ^3     1. Given
2.^1 c ^3                        2. Transitive prop. of congruence
3. m^1 = m^3                      3. ?
4.m^1 = 40                       4.Substitution prop. of equality
3.    Transitive prop. Of congruence
      Def. of congruent angles
      Substitution prop. Of equality
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