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Algebra Reasons Addition Property Subtraction Property Multiplication Property Division Property Distributive Property 2(x + y) = 2x + 2y Reflexive Property x = x Substitution Property
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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
• Subtraction Property
• Multiplication Property
• Division Property
• Distributive Property
2(x + y) = 2x + 2y
• Reflexive Propertyx = x
• Substitution Property
Justify each step in solving the equation.
23 45yy
15 20 2y y
13 20 0y
13 20y
2013
y
Multiplication Property
Subtraction Property
Subtraction Property
Division Property
Given
Justify each step in solving the equation.
6 12x x
7 12x
127
x
Given
Multiplication Property
Addition Property
Division Property
3 𝑥=6− 12 𝑥
First Geometry Proof YEAH!Given :Prove : 1 3
m AOC m BODm m
321
O
AB
C
D
Given :Prove : 1 3
m AOC m BODm m
STATEMENTS REASONS1. Given
2. Angle Addition Postulate
3. Substitution Prop
4. Subtraction Prop
321
O
AB
C
D
1. 𝑚∠𝐴𝑂𝐶=𝑚∠𝐵𝑂𝐷2. 𝑚∠𝐴𝑂𝐶=𝑚∠1+𝑚∠2 ; 𝑚∠𝐵𝑂𝐷=𝑚∠2+𝑚∠3
3. 𝑚∠1+𝑚∠2=𝑚∠ 2+𝑚∠3
4. 𝑚∠1=𝑚∠3
Try AnotherGiven : ;Prove :
ST RN IT RUSI UN
S I T
NUR
STATEMENTS REASONS
Given : ;Prove :
ST RN IT RUSI UN
S I T
NUR
1. Given
2. ; ST SI ITRN RU UN
2. Segment Addition Postulate
3. SI IT RU UN 3. Substitution Prop
4. Subtraction Prop
1. 𝑆𝑇=𝑅𝑁 ; 𝐼𝑇=𝑅𝑈
4. 𝑆𝐼=𝑈𝑁