Geometry Midterm Theorems, Postulates, Definitions, And Corollaries

 
Created Jul 16, 2009
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atewhs
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Side ASide B
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...
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...
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...
5 ways to prove two lines are parallel
1. show that corresponding angles are congruent 2. show that alternate interior angles are...
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...


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