# Algebra Proofs by ert554898

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```									  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
Segments
• 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
Exercise
•    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
segments
5.sJK c sJL      5. Given
6. sLK c sJL.    6.Transitive Prop.
Of Congruence
Proving Statements

• 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.
Example
• 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
Exercise
•    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