Introduction to Proofs-Geometry

Reflexive Property

X=X

Symmetric Property

If X=Y then Y=X

Transitive Property

If X=Y and Y=Z then X=Z

Addition POE

If X=Y then X+Z=Y+Z

Subtraction POE

If X=Y then X-Z=Y-Z

Multiplication POE

If X=Y then XxZ=YxZ

Division POE

If X=Y then X/Z=Y/Z

Substitution POE

If X=Y then Y can be substituted for X in any expression

Distributive POE

If X(Y=Z)=XY + XZ which also proves combining like terms

Reflexive Property of Congruence

line AB is congruent to line AB,

AB ≅ AB,

Symmetric Property of Congruence

if AB ≅ CD, then CD ≅ AB

if

Transitive Property of Congruence

if ∠A≅∠B, and ∠B≅∠C,

then ∠A≅∠C,

Fig a ≅ Fig b and Fig a ≅ Fig c--> Fig a ≅ Fig c

Vertical Angles Theorem

Vertical angles are congruent If Angle 1 and Angle 3 are congruent than Angle 2 and Angle 4 are congruent

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Angle Bisector

a ray that divides an angle into two congruent angles

Angle Addition Postulate

If R is in the interior of

Transitive Property of Congruence

if ∠A≅∠B, and ∠B≅∠C,

then ∠A≅∠C and/or

— ~ —

If AB = CD, and

— ~ —

CD = EF, then

— ~ —

AB = EF

Law of Detachment

If the hypothesis of a true conditional is true, then the conclusion is true.

Law of Syllogism

when p->q is true, and q->r is true, then p->r is true

Angle Bisector

a ray that divides an angle into two angles that are congruent

Definition of Complimentary Angles

Sum of 2 angles is 90*

Definition of Supplementary Angles

two angles whose measures have the sum of 180'

Segment Addition Postulate

If three points, A,B, and C are collinear and B is between A and C, then AB + BC= AC

Ruler Postulate

Every point on a line can be paired with a real number.

Congruent Supplements Theorem

If 2 angles are supplementary to the same angle, then the 2 angles are congruent.

Right Angle Congruence Theorem

All Right Angles are congruent.

Definition of Right Angle

An angle with a measure equal to 90 degrees.

Definition of Congruent Angles

Angles that have the same measure.

Definition of Congruent Segments

Segments that have the same length.

Definition of midpoint.

The point that divides or bisects a segment into two congruent segments. M is midpoint of Line AB so AM=MB and Line AM is congruent to MB.