1. 2.6 Deductive Reasoning
GEOMETRY

2. Special Pairs of Angles
Vertical angles
Linear pair of angles
Complementary angles
Supplementary angles

3. Vertical Angles Definition: If two angles have their sides
that form two pairs of opposite rays, then the
two angles are vertical angles.
VERTICAL ANGLES THEOREM:
If two angles are vertical angles, then they are congruent.

4. Linear Pair Definition: If two angles are adjacent and their noncommon
Sides are opposite rays, then the two angles form a linear pair.
LINEAR PAIR POSTULATE:
If two angles for a linear pair, then
They are supplementary
The sum of their measures is 180o.

5. Complementary Angles Definition: If two angles have a sum of 90o,
then the two angles are complementary angles.
Each angle is the complement of the other.
The angles themselves do not have to be adjacent,
but if they are, they must form a “perfect” corner.

6. Congruent Complements Theorem
If two angles are complementary to the same
or to congruent angles,
Then the two angles are congruent.
If A and B are complementary
and C and B are complementary
then A  C because both A and C
are complementary to B.

7. Supplementary Angles Definition: If two angles have a sum of 180o,
then the two angles are complementary angles.
Each angle is the supplement of the other.
The angles themselves do not have to be adjacent,
but if they are, they must form a straight line.

8. Congruent Supplements Theorem
If two angles are supplementary to the same
or to congruent angles,
Then the two angles are congruent.
If A and B are supplementary
and C and B are supplementary
then A  C because both A and C
are supplementary to B.