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Segment Addition Postulate

two segments add up to one bigger
segment


Angle Addition Postulate

two angles add up to one bigger angle


Postulate 5

a line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one line


Postulate 6

Through any two points there is exactly one line.


Postulate 7

Through any three points there is exactly one plane, and through any three collinear points there is exactly one plane.


Postulate 8

if two points are in a plane, then the line that contains the points is in that plane.


Postulate 9

If two points intersect, their intersection is a line.


Theorem 11

If two lines intersect, then they intersect in exactly one point.


Theorem 12

Through a line and a point not in the line there is exactly one plane.


Theorem 13

If two lines intersect, then exactly one plane contains the lines.


Addition Property

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


Subtraction Property

If a = b and c = d then a  c = b  d


Multiplication Property

If a = b, then ca =cb


Division Property

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


Substitution Property

if a = b, then a or b can be substituted for the other in any equation or inequality.


Reflexive Property

a = a


Symmetric Property

If a = b, then b = a.


Transitive Property

If a = b, and b = c, then a = c.


Midpoint Theorem

If M is the midpoint of AB, then AM = 1/2AB


Angle Bisector Theorem

If BX is the bisector of <ABC, then m<ABX = 1/2<ABC


Definition of vertical angles

vertical angles are congruent


Definition of Perpendicular Lines

if lines form congruent adjacent angles or right angles


corresponding angles

corresponding angles are congruent


alternate interior angles

alternate interior angels are congruent.


SSI angles

same side interior angles are supplementary


definition of perpendicular lines

If a transversal is perpendicular to one of two paralell lines then it is perpendicular to the other one too.


5 ways to prove two lines are parallel

1. show that corresponding angles are congruent 2. show that alternate interior angles are congruent 3. show that same side interior angles are supplementary 4. show both lines are perpendicular to a third line 5. show that both lines are parallel to a third line 

Theorem 38

through a point outside a line, there is exactly one line parallel to the given line.


Theorem 39

Through a point outside a line, there is exactly one line perpendicular to the given line.


Theorem 310

Two lines parallel to a third line are parallel to each other.


Corollary

If two angles of a triangle are congruent to two angles of another triangle, then the triangles are congruent.
