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Term/Theorem
Definition/Description
Proof Reason
Chapter 2
Angle Addition Postulate
m  AOB+m  BOC=m  AOC
Angle Addition Postulate
Segment Addition Postulate
AB + BC = AC
Segment Addition Postulate
Midpoint
A point that divides a segment into 2
congruent segments
Definition of midpoint
Segment Bisector
Divides a segment into 2 congruent
segments
Definition of Segment Bisector
Angle Bisector
A ray that divides an angle into two
congruent coplanar angles
Definition of Angle Bisector
Vertical  ’s are 
Vertical Angle Theorem
Vertical angles are congruent
Complementary Angles
Two angles whose measures have a sum
of 90
Definition of Complementary
Angles
Supplementary Angles
Two angles whose measures have a sum
of 180
Definition of Supplementary
Angles
Linear Pair
Two adjacent angles that form a line (are
supplementary)
Definition of Linear Pair
Right Angle Theorem
All right angles are congruent
Addition Prop. Of Equality
If a = b, then a + c = b + c
Subtraction Prop. Of Equality
If a = b, then a – c = b – c
Division Prop. Of Equality
Mult. Prop of Equality
Simplify -ORCombine Like Terms
If a = b and c  0, then
a b

c c
If a = b, then ac = bc
3x + 4x + 7 = 19
7x + 7 = 19
All right  ’s are 
Add Prop of =
Subtraction Prop of =
Div Prop of =
Mult Prop of =
Simplify -ORCombine Like Terms (CLT)
Distributive Property
Substitution
Reflexive
Symmetric
Transitive
Congruent Supplements Thm.
Congruent Complements
Thm.
a ( b + c ) = ab + ac
Distributive Property
If a = b then b can replace a in any
expression.
Substitution Property
a=a
A  A
Reflexive Property of =
Reflexive Property of 
If a = b, then b = a
If AB  CD then CD  AB
Symmetric Property of =
Symmetric Property of 
If a = b and b = c, then a = c.
If A  B and B  C then
A  C
Transitive Property of =
Transitive Property of 
If  s are supp to the same  ,
If two angles are supplements of the
then they are 
same angle (or of congruent angles), then ------------------OR------------------the two angles are congruent
If  s are supp to   s, then
they are 
If  s are comp to the same  ,
If two angles are complements of the
then they are 
same angle (or of congruent angles), then ------------------OR------------------the two angles are congruent
If  s are comp to   s, then
they are 
Chapter 3
Perpendicular lines form right angles.
Perpendicular Lines
Corresponding Angles Post.
Alt. Interior Angles Thm
Alt. Exterior Angles Thm
Same Side Interior Angles
Thm
Same Side Exterior Angles
Thm
Conv. Of Corresponding
Angles Post
Lines that form right angles are
perpendicular.
If a transversal intersects two parallel
lines, then corresponding angles are
congruent
If a transversal intersects two parallel
lines, then Alt. interior angles are
congruent
If a transversal intersects two parallel
lines, then Alt. exterior angles are
congruent
If a transversal intersects two parallel
lines, then same side interior angles are
supplementary
If a transversal intersects two parallel
lines, then same side exterior angles are
supplementary
If two lines and a transversal form
corresponding angles, then the lines are
parallel.
Definition of 
If
lines  corresp  s 
If
lines  alt. int.  s 
If
lines  alt. ext.  s 
If lines  same side int  s are
supp
If lines  same side ext  s
are supp
If  corresp  s  lines
Conv. Of Alt. Interior Angles
Thm.
Conv of Alt. Exterior Angles
Thm
Conv of Same Side Interior
Angles Thm
Conv of Same Side Exterior
Angles Thm
Theorem 3-9
Theorem 3-10
Theorem 3-11
Triangle Angle Sum Theorem
If two lines and a transversal form
alternate interior angles that are
congruent, then the lines are parallel
If two lines and a transversal form
alternate exterior angles that are
congruent, then the lines are parallel
If two lines and a transversal form same
side interior angles that are
supplementary, then the lines are parallel
If two lines and a transversal form same
side exterior angles that are
supplementary, then lines are parallel
If two lines are parallel to the same line,
then they are parallel to each other
In a plane, if two lines are perpendicular
to the same line, then they are parallel to
each other
In a plane, if a line is perpendicular to
one of two parallel lines, then it is
perpendicular the other
The sum of the measures of the angles of
a triangle is 180
Polygon Angle Sum Theorem
The measure of each exterior angle of a
triangle equals the sum of the measures
of its two remote interior angles
The sum of the measures of an n-gon is
(n – 2)180
Polygon Exterior Angle Sum
Theorem
The sum of the measures of the exterior
angles of a polygon, one at each vertex,
is 360
Triangle Exterior Angle
Theorem
If  alt int  s  lines
If  alt ext  s  lines
If supp same side int  s 
lines
If supp same side ext  s 
lines
If lines are || to the same line, then
they are ||
If two lines are  to the same
line, then they are ||
If a line is  to one of two || lines,
then it is  the other
Sum of  s of a Δ is 180
Δ ext  = sum of remote int  s
Sum of  s of an n-gon is
(n – 2)180
Sum of ext.  s is 360
Chapter 4
Theorem 4.1
Definition of congruent
polygons
Side-Side-Side Postulate
Side-Angle-Side Postulate
If two angles of one triangle are congruent to
two angles of another triangle, then the third
angles are congruent
If all corresponding angles and all
corresponding sides are congruent, then the
polygons are congruent
If 2  s in a Δ are  , then 3rd  s
are 
Definition of  (name polygon)
If the three sides of one triangle are
congruent to the three sides of another
triangle, then the triangles are congruent.
SSS
If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the
triangles are congruent
SAS
Angle-Side-Angle Postulate
Angle-Angle-Side Theorem
Definition of Right Triangle
Hypotenuse-Leg Theorem
Corresponding Parts of
Congruent Triangles are
Congruent
Definition of Isosceles
Triangle
Isosceles Triangle Theorem
If two angles and the included side of one
triangle are congruent to two angles and the
included side of another triangle, then the
triangles are congruent
If two angles and nonincluded side of one
triangle are congruent to two angles and
nonincluded side of another triangle, then the
triangles are congruent
If a triangle has a right angle, then it is a
right triangle.
If the hypotenuse and a leg of one right
triangle are congruent to the hypotenuse
and leg of another right triangle, then the
triangles are congruent.
If triangles are proven congruent the
their corresponding sides and angles are
congruent
If a triangle has two congruent sides,
then it is am isosceles triangle.
In a triangle if two sides are congruent,
then opposite angles are congruent.
Corollary to Theorem 4-3
If two angles of a triangle are congruent,
then the sides opposite the angles are
congruent.
The bisector of the vertex angle of an
isosceles triangle is the perpendicular
bisector of the base.
If a perpendicular bisector goes the
vertex of a triangle, then the triangle is
isosceles.
If a triangle is equilateral, then it is
equiangular.
Corollary to Theorem 4-4
If a triangle is equiangular, then it is
equilateral.
Converse Isosceles Triangle
Theorem
Theorem 4-5
Converse of Theorem 4-5
ASA
AAS
Definition of Right Triangle
HL
CPCTC
Definition of Isosceles Triangle
Term/Theorem
Definition/Description
Chapter 6
Proof Reason
Theorem 6-1
Opposite sides of a parallelogram are
congruent
If
 opp. sides 
Theorem 6-2
Opposite angles of a parallelogram are
congruent.
If
 opp. angles 
Theorem 6-3
The diagonals of a parallelogram bisect
each other.
Theorem 6-5
Theorem 6-6
Theorem 6-7
Theorem 6-8
If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
If both pairs of opposite angles of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
If the diagonals of a quadrilateral bisect
each other, then the quadrilateral is a
parallelogram.
If one pair of opposite sides of a
quadrilateral is both congruent and
parallel then the quadrilateral is a
parallelogram.
 diagonals bisect each
other
If
If both opp. sides  
If both opp. angles  
If diagonals bisect each other 
If one pair opp. sides  and
Theorem 6-9
Each diagonal of a rhombus bisects two
angles of the rhombus.
Theorem 6-10
The diagonals of a rhombus are
perpendicular.
Theorem 6-11
The diagonals of a rectangle are
congruent.
Theorem 6-12
If one diagonal of a parallelogram bisects
two angles of the parallelogram, the
parallelogram is a rhombus.
Theorem 6-13
If the diagonals of a parallelogram are
perpendicular, then the parallelogram is a rhombus.
Theorem 6-14
If the diagonals of a parallelogram are congruent,
then the parallelogram is a rectangle.
If diags.   rect
Theorem 6-15
The base angles of an isosceles trapezoid
are congruent.
If iso. trap  base  
Theorem 6-16
The diagonals of an isosceles trapezoid
are congruent.
If iso. trap  diags. 
Theorem 6-17
The diagonals of a kite are perpendicular.
If kite  diags. 

 diag. bisect opp. 
If
If
 diag. are 
If rect.  diag. 
If diag. bisects 2  of

If diag. are  