Download Tools for Proofs

Tools for Proofs
Chapters 1-2
To prove a statement you may use:
 Definitions - uses known words to describe a new word.
 Properties- a quality
 Postulates- rules that are accepted without proof.
 Theorems- a true statement that follows as a result of other true statements
The tools we’ve already used are organized below.
You can add definitions, properties, postulates and theorems as you continue to work in future chapters. Pages 827-832
have the postulates and theorems listed.
Definitions
Point, line, plane
Properties
Addition Property of Equality
Collinear
Subtraction Property of Equality
Coplanar
Multiplication Property of Equality
Line segment
Division Property of Equality
ray , opposite rays
Distributive Property
congruent
Reflexive Property
midpoint, bisect
Symmetric Property
vertical angles
Transitive Property
linear pair
Substitution Property
complementary and supplementary
perpendicular
parallel
Geometry
Page 1
Postulates
1. Ruler Postulate
Theorems
 Properties of Segment
2. Segment Addition Postulate
Congruence
3. Protractor Postulate
- reflexive, symmetric and
4. Angle Addition Postulate
5. Through any two points there is
transitive
 Properties of Angle Congruence
exactly one line.
– reflexive, symmetric and
6. A line contains at least two points.
transitive
7. If two lines intersect, then their
intersection is exactly one point.
8. Through any three noncollinear
points there exists exactly one plane.
9. A plane contains at least three
noncollinear points.
10. If two points lie in a plane, then the
 Right Angle Congruence
Theorem
 Congruent Supplements
Theorem
 Congruent Complements
Theorem
 Vertical Angles Theorem
line containing them lies in the plane.
11. If two planes intersect, then their
intersection is a line.
12. Linear Pair Postulate
Geometry
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