Download Reasons for Proofs

REASONS FOR PROOFS
Algebra Reasons









Addition Property: Adding the same term to both sides of an equation
Subtraction Property: Subtracting the same term to both sides of an equation
Multiplication Property: Multiplying the same term to both sides of an equation
Division Property: Dividing the same term to both sides of an equation
Distributive Property : a(b+c)=ab+ac
Substitution Property: If a=b, then either a or b may be substituted for the other in any
equation (or inequality)
Reflexive Property: Ex. a = a
D  D
DE  DE
Symmetric Property: If a=b then b=a
If DE  FG then FG  DE
Transitive Property: If a=b and b=c, then a=c
 Justify Each statement with a property from algebra or a property of congruence
1. If AB=CD and CD=EF, then AB=EF
2. If RS=TW, then TW=RS
3. If x+5=16, then x=11
4. AB = AB
5. If 5y=-20, then y=-4
6. If z/5=10, then z=50
7. 2(a+b)=2a+2b
8. If 2z-5=-3, then 2z=2
9. If 2x+y=70 and y=3x, then 2x+3x=70
10. If AB=CD, CD=EF and EF=23, then AB=23
Geometry Reasons

Angle Addition Postulate:
If C is in the interior of ABD, then mABC + mCBD = mABD.
mABD = 76
mABC + mCBD = 76

Segment Addition Postulate:
If C is between A and B, then AC + CB = AB.

Definition of midpoint
If M is the midpoint of AB, then AM = MB.

Midpoint Theorem
If M is the midpoint of AB, then AM = 1/2AB and MB = 1/2AB.

Definition of Angle Bisector
If JK bisects LJM, then mLJK = mKJM.

Angle Bisector Theorem
If JK bisects LJM, then mLJK = 1/2mLJM and mKJM = 1/2mLJM.

Definition of Complementary Angles
If 1 and 2 are complementary angles, then m1 + m2 = 90.

Definition of Supplementary Angles
If 1 and 2 are supplementary angles, then m1 + m2 = 180.

Vertical Angle Theorem
Vertical angles are congruent.
1  2

Definition of Right Angle
If ABC is a right angle, then mABC = 90.

Definition of Straight Angle
If DEF is a straight angle, then mDEF = 180.