Geometry Midterm Theorems, Postulates, Definitions, And Corollaries

Geometry Midterm Theorems, Postulates, Definitions, And Corollaries
  
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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 1-1
 
If two lines intersect, then they intersect in exactly one point.
Theorem 1-2
 
Through a line and a point not in the line there is exactly one plane.
Theorem 1-3
 
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 3-8
 
through a point outside a line, there is exactly one line parallel to the given line.
Theorem 3-9
 
Through a point outside a line, there is exactly one line perpendicular to the given line.
Theorem 3-10
 
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.

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