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GEOMETRY TOOLBOX
PROPERTIES OF EQUALITY
Addition
 Reflexive
Subtraction
 Symmetric
Multiplication
 Transitive
Division
 Substitution
PROPERTIES OF CONGRUENCE
 Reflexive
 Symmetric
 Transitive
CHAPTERS 1-3
ANGLES
Definition of congruent angles

Definition of angle bisector

 Every point on an angle bisector is
equidistant from the sides of the angle.
Angle Addition Postulate

Angle Bisector Theorem

Definition of a right angle

 All right angles are congruent.
Definition of a straight angle.

If the exterior sides of adjacent angles lie in a

line, then the angles are supplementary.
LINE SEGMENTS
 Definition of congruent segments
 Definition of segment bisector
 Segment Addition Postulate
 Midpoint Theorem
 Definition of midpoint
PERPENDICULAR LINES
 Definition of perpendiculars
 Lines are perpendicular if and only if they form
congruent adjacent angles.
 If the exterior sides of two adjacent angles are
perpendicular, the angles are complementary.
PARALLEL LINES
If two parallels are cut by a transversal:
 alternate interior angles are congruent.
 corresponding angles are congruent.
 same-side interior angles are supplementary.
Two lines are parallel if:
 alternate interior angles are congruent.
 corresponding angles are congruent
 same-side interior angles are supplementary.


they are parallel to a third line.
they are perpendicular to the same line.
CONDITIONAL STATEMENTS
 hypothesis, conclusion
 biconditional
 converse, inverse, contrapositive
deductive reasoning
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Vertical angles are congruent
Definition of complementary angles
Definition of supplementary angles
Complements of congruent angles are congruent
Complements of the same angle are congruent
Supplements of congruent angles are congruent
Supplements of the same angle are congruent
TRIANGLES
 The sum of the angles in a triangle equals 180
 If two angles of one triangle are congruent to
two angles of another triangle, the third
angles are congruent.
 The measure of an exterior angle of a triangle
equals the sum of the two non-adjacent
interior angles.
 Definition of a right triangle
 Acute angles of a right triangle are
complementary
 Definition of an isosceles triangle.
 Isosceles Triangle Theorem
 An equilateral triangle is equiangular.
REGULAR CONVEX POLYGONS (with n sides)
 The sum of the interior angles   n  2 180
 n  2 180

Each interior angle 

The sum of the exterior angels  360

Each exterior angle 

At any vertex, the sum of the interior and the
Exterior angles  180


Chapters 1-2
Chapter 3
n
360
n