Download Common Core Geometry - Honors Postulates and Theorems

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Common Core Geometry - Honors
Date: _____________
Postulates and Theorems
Commonly Used Terms
1) Postulate: A statement whose truth value is accepted without proof.
2) Theorem: A statement that is proved through deductive reasoning.
3) Deductive reasoning: Using the fact to formulate conclusions that must be true.
Properties and Postulates
1) Addition Postulate:
2) Subtraction Postulate:
3) Partition Postulate:
4) Substitution Property:
5) Multiplication Postulate:
6) Division Postulate:
7) Reflexive Property:
8) Transitive Property:
Theorems
1) Midpoint: divides a segment into two congruent segments.
2) Bisector of a segment or an angle: divides a segment or angle into two congruent halves.
3) Median of a triangle: A line segment that joins any vertex of a triangle to the midpoint of
the opposite side.
4) Altitude of a triangle:
a.)
b.)
c.)
5) a) Perpendicular lines form right angles.
b) All right angles are congruent
6) Vertical angles are congruent.
7) If two angles form a linear pair, they are supplementary.
8) If two angles are compliments to the same angle, they are congruent to each other.
9) Compliments of congruent angles are congruent.
10) If 2 angles are supplements to the same angle, they are congruent to each other.
11) Supplements of congruent angles are congruent.
12) If two sides of a triangle are
, the angles
these sides are congruent.
13) If two angles of a triangle are congruent, the sides opposite these angles are congruent.