Proofs Geometry

Proofs and rules needed for Geometry

Addition Property of Equality

If a=b, then a+c=b+c

Subtraction Property of Equality

If a=b, then a-c=b-c

Multiplication Property of Equality

If a=b, then ac=bc

Division Property of equality

If a=b, then a/c=b/c

Reflixive Property

a=a

Symmetric Property

a=b then b=a

Transitive Property

a=b b=c then a=c

Distributive Property

a(b+c)=ab+ac

Substitution Property

If x=y, then x can be substituted in any problem with y

Angle Addition Postulate

angle ABC+ angle CBD=ABD

Segement Addition Postulate

AB+BC=AC

Vertical Angles Theorem

Vertical angles are congruent

Definition of Midpoint

AM=MB

Definition of Perpendicular Lines

Lines that intersect to from right angles

Definition of a Right Angle

Angle measure is 90 degrees

Definition of Supplementary Angles

Angles whose measurements add up to 180 degrees

Definition of Complementary Angles

Angles whose measurements add up to 90 degrees

Definition of Congruence

Two figures with the same size/shape

Corresponding Angles

Angles 2 & 6 or 4 & 7

Alternate Interior Angles

Angles 3 & 5 or 4 &6

Same-Side(Consecutive) Interior Angles

Angles 3 & 6 or 4 & 5

Corresponding Angles Postulate

Corresponding angles are congruent

Alternate Interior Angles Theorem

Alternate interior angles are congruent

Same-side Interior Angles Theorem

Same-side interior angles are supplementary