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They are easier than Geometry ones!!
PROOFS
• The “GIVEN” is always written first
– It is a “GIMME”
• The “PROVE” should be your last line
• Make a two column proof with Steps and
Reasons
Algebra Reasons
• Addition Property
• Distributive Property
2(x + y) = 2x + 2y
• Subtraction Property
• Reflexive Property
• Multiplication Property
x=x
• Division Property
• Substitution Property
Justify each step in solving the
equation.
2y
3y  4 
5
Given
15 y  20  2 y
Multiplication Property
13 y  20  0
Subtraction Property
13 y  20
Subtraction Property
20
y
13
Division Property
Justify each step in solving the equation.
1
3𝑥 = 6 − 𝑥 Given
2
6x  12  x
Multiplication Property
7 x  12
Addition Property
12
x
7
Division Property
First Geometry Proof YEAH!
Given : mAOC  mBOD
Prove : m1  m3
B
A
C
D
1
O
2
3
Given : mAOC  mBOD
Prove : m1  m3
B
A
C
D
1
2
3
O
STATEMENTS
1. 𝑚∠𝐴𝑂𝐶 = 𝑚∠𝐵𝑂𝐷
REASONS
1. Given
2. 𝑚∠𝐴𝑂𝐶 = 𝑚∠1 + 𝑚∠2; 2. Angle Addition Postulate
𝑚∠𝐵𝑂𝐷 = 𝑚∠2 + 𝑚∠3
3. 𝑚∠1 + 𝑚∠2 = 𝑚∠2 + 𝑚∠3
4. 𝑚∠1 = 𝑚∠3
3. Substitution Prop
4. Subtraction Prop
Try Another
Given : ST  RN ; IT  RU
Prove : SI  UN
S
R
I
U
T
N
Given : ST  RN ; IT  RU
Prove : SI  UN
S
I
R
STATEMENTS
U
REASONS
1. 𝑆𝑇 = 𝑅𝑁; 𝐼𝑇 = 𝑅𝑈 1. Given
2. ST  SI  IT ;
RN  RU  UN
2. Segment Addition
3. SI  IT  RU  UN
3. Substitution Prop
4. 𝑆𝐼 = 𝑈𝑁
4. Subtraction Prop
Postulate
T
N