1. UNIT Algebraic Proofs
A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.
An important part of writing a proof is giving justifications to show that every step is valid.

2. Solve for x given 3(x -1) – 3 = 11.
UNIT Algebraic Proofs
Solve for x given 3(x -1) – 3 = 11.
Justify each step!

3. Properties of Equality see page 104
UNIT Algebraic Proofs
Properties of Equality see page 104
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 a•c = b•c
Division Property……....If a=b and c0, then ac = bc
Reflexive Property……..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 b can replace a in
any expression.
Distributive Property…..a(b + c) = a•b + a•c not on 104

4. Properties of Congruence see page 106
UNIT Algebraic Proofs
Earlier we said geometric figures, like segment and angles are congruent instead of equal (XY  WV).
Since numbers are different than figures, we must have some properties of congruence for those figures.
Properties of Congruence see page 106
Reflexive Property of Congruence……EF  EF
Symmetric Property of Congruence….if 12 then 21
Transitive Property of Congruence…...if AB  CD and CD  EF,
then AB  EF

5. Name the property illustrated in each statement
UNIT Algebraic Proofs
Name the property illustrated in each statement
a. If x = y and y + 4 = 3x, then x + 4 = 3x.
The property is the Substitution Prop. of Equality.
b. If x + 4 = 3x, then 4 = 2x.
The property is the Subtraction Prop. of Equality.
c. If P Q, Q R, and R S,
then P S.
Transitive Property of Congruence.
d. If ST UV then UV ST
Symmetric Property of Congruence.

6. UNIT Algebraic Proofs
Review properties on page 104 and 106.
Then name the property that justifies each statement.
If AB = CD, then AB + XY = CD + XY
If XD = FY and FY = 12, then XD = 12
If XY + JM = GT + XY, then JM = GT
If 2(mABC) = 180, then mABC = 90
RS = RS
If mABC = 25, then 25 = mABC
Use the given property to complete each statement.
Symmetric Prop of Eq If MN = UT, then ________
Div. Prop of Eq If 4mQWR= 120, then ________
Transitive Prop of Eq If SB=VT and VT=MN, then _______
Add. Prop of Eq If y-15 = 36, then y-10 = _________
Reflexive Prop of Eq JL ≌ _________
Substitution Prop of Eq. If 2x+3a=7 and 3a=2, then________

7. UNIT Algebraic Proofs
Solve for x and write a justification for each step.
NO = NM + MO
Segment Addition Post.
4x – 4 = 2x + (3x – 9)
Substitution Property of Equality
4x – 4 = 5x – 9
Simplify.
–4 = x – 9
Subtraction Property of Equality
5 = x
Addition Property of Equality

8. UNIT Algebraic Proofs
Solve for x and write a justification for each step.
ABD + DBC = ABC
AAP
(3x + 5) + (6x – 16) = 8x
Subst
9x - 11= 8x
Simplify
x - 11= 0
SPE
x = 11
APE

9. Homework:
2.5(107): 16,21,23,25-28,34