Definitions, Postulates and Theorems for Proofs

Segment Addition Postulate

AB + BC = AC

Angle Addition Postulate

m angle ABD + m angle DBC = m angle ABC

Definition of congruence

Used to switch between equal sign and congruence sign

Angle/ segment bisector

Divides into two equal parts

Line contains how many points?

2

Plane contains how many points?

3 noncollinear

Space contains how many points?

4 non coplanar

How many lines thru 2 points

Exactly 1

relation between collinear and planes

collinear = many planes, noncollinear = 1 plane

Intersection of 2 planes

1 line

Intersection of 2 distinct lines

point

intersection of 3 or more planes

line or point

how many planes for a line and a seperate point

1 plane

If 2 lines intersect, how many planes are there

1 plane

Addition POE

if A=B , A+C = A+B

Subtractiojn POE

If A=B, A-C=B-C

Multiplication POE

If A=B, AC=BC

Division POE

If A=B and C is not 0, A/C=B/C

Substitution POE

If A=B, it can be replaced by A

Transitive POE/C

If A=B and B=C, then A=C

Distributive POE

A(B+C) = AB+AC

Reflexive POE/C

A=A

Symmetric POE/C

if A=B, then B=A

Definition of a midpoint

if m is midpoint of line AB, then AM is congruent to MB

Definition of Angle Bisector

if ray BX bisects angle ABC, then angle ABC is congruent to angle CBX

Midpoint Theorem

If m is the midpoint of line AB, then AM=1/2AB and MB=1/2AB

Angle Bisector Theorem

If ray BX bisects angle ABC, then angle ABX=1/2ABC and angle BXC=1/2ABC

Definition of Complementary

2 angles that add up to 90 degrees.

Definition of Supplementary

2 angles that add up to 180 degrees

Vertical angle theorem

Vertical angles are congruent

Definition of perpendicular lines

2 intersecting lines that form right angles

What is formed if two lines are perpendicular?

Congruent, adjacent angles

If two angles are supplements or complements of the congruent or same angle….

they are congruent

Definition of parallel lines

Coplanar lines that dont intersect

Definition of skew lines

noncoplanar lines that dont intersect

Definition of parallel planes

planes that don’t intersect

Definition of transversal

A line that intersects 2 or more coplanar lines in different points

If 2 parallel lines are cut bh a 3rd plane what is the relation between the lines of intersection?

They are parallel

Alternate interior angle theorem

If 2 parallel lines are cut by a transversal, the alternate interior angles are congruent

Same side/consecutive interior angle theorem

If 2 parallel lines are cut by a transversal, then the same side interior angles are SUPPLEMENTARY

Alternate exterior angle theorem

If 2 parallel lines are cut by a transversal, then the alternate exterior angles are congruent

Corresponding angle postulate

If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent