# Unit 1: Introduction To Geometry Notes Day 6 Algebraic Proofs Worksheet With Answers

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Geometry Support Unit 1—Introduction to Geometry Notes
Name_____________________________
Date__________________
Day 6—Algebraic Proofs
1. Solve the following equation. 2. Rewrite your proof so it is “formal”
proof. Justify each step as you solve it.
2(4x - 3) – 8 = 4 + 2x 2(4x - 3) – 8 = 4 + 2x
Proof: An argument that uses logic, definitions, properties, and previously proven statements
to show a conclusion is true
Postulate: Statement that are accepted as true without proof.
Theorem: Statement that can be proven true.
Two Column Proofs
• ______________________________________________
• ______________________________________________
• ______________________________________________
Geometry Support Unit 1—Introduction to Geometry Notes
Name of
Property
Statement of
Property
Example Student Version
M
o
s
t
H
e
lp
fu
l
Addition
Property
of Equality
If a = b, then
a + c = b + c
I can add the same
thing to both sides of
an equation without
changing the
solutions.
Subtraction
Property
of Equality
If a = b, then
a – c = b – c
I can subtract the
same thing from both
sides of an equation
without changing the
solutions.
Multiplication
Property
of Equality
If a = b, then
ac = bc
I can multiply both
sides of an equation
by the same number
(other than 0) without
changing the
solutions.
Division
Property
of Equality
If a = b and c 0, then
a / c = b / c
I can divide both sides
of an equation by the
same number (other
than 0) without
changing the
solutions.
Distributive
Property
of Equality
For any real numbers a,
b, and c:
a (b + c) = ab + ac
I can distribute a
number outside
parentheses to each
term inside
parentheses without
changing the meaning
of the expression.
Simplify
(Combine Like
Terms)
For any real numbers a,
b, and x:
ax + bx = (a + b)x
I can combine like
terms without
changing the eaning
of the expression. Symmetric
Property
of Equality
If a = b, then
b = a
I can swap the sides
of an equation without
changing the
solutions.
H
e
lp
fu
l
in
G
e
o
m
e
tr
y
Reflexive
Property
of Equality
For any real number a:
a = a
Any number is equal
to itself.
Transitive
Property
of Equality
If a = b and b = c,
then a = c
If I’m the same as
Chris and Chris is the
same as Pat,
then I’m the same as
Pat.
Substitution
Property
of Equality
If a = b, then a can be
substituted
for b in any expression
or equation
If I know the value of
a variable, I can
substitute that into
other expressions and
equations.
Geometry Support Unit 1—Introduction to Geometry Notes
Fill in the blanks to finish the proofs.
1. Given: 5 18 3 2x x− = +
Prove: 10x =
2. Given:
2 6
8
3
x −
=
Prove: 15x =
3. Given: 4(5 7) 3 12 27x x x+ − = −
Prove: 11x = −
Statements Reasons
1. 1. Given
2. 5 3 20x x= + 2.
3. 3. Subtraction Property
4. 4. Division Property
Statements Reasons
1.
1.
2. 2. Multiplication Property
3. 2 30x = 3. Addition Property
4. 15x = 4.
Statements Reasons
1. 4(5 7) 3 12 27x x x+ − = −
1.
2. 20 28 3 12 27x x x+ − = − 2.
3. 3. Combine like terms
4. 4. Subtraction Property
5. 5. Subtraction Property
6. 11x = − 6.
Geometry Support Unit 1—Introduction to Geometry Notes
4. Given: 6x – 4 = 3x + 8.
Prove: x = 4
Statement Reason
5. Given: 48 = 5(2x – 7) + 3.
Prove: x = 8
Statement Reason
6. Solve
5
2
8
x +
= .
Prove: x = 11
Statement Reason
STATEMENTS REASONS
Geometry Support Unit 1—Introduction to Geometry Notes
7. Given: 11 3( 4) 2x= − +
Prove: 7x =
8. Given: 2(3 6) 4 2x x− − = +
Prove: 1x =
9. Given:
2 6
12
4
x +
=
Prove: 21x =