3.  Deductive Reasoning is a process of reasoning logically from given facts to a conclusion.  Addition Property of equality if a=b then a+c=b+c  Subtraction Property of equality if a=b then a-c=b-c  Multiplication Property of equality if a = b then ac = bc  Division Property of equality if a=b then a/c = b/c c≠0

4.  Substitution Property– if a=b, then b can replace a in any expression  Distributive Property – a(b+c) = ab + ac  Reflexive Property AB = AB  Symmetric Property if AB = CD then CD = AB  Transitive Property if AB = CD & CD = EF then AB = EF

5.  Draw two intersecting lines.  Fold the sides of <1 onto <2. What do you notice?  Fold the sides of <3 onto <4. what do you notice?  Make a conjecture about the angles formed by two intersecting lines. 1 2 4 3

6.  Vertical angles – two whose sides are opposite rays.  Adjacent angles – two coplanar angles with a common vertex, no common interior points.  Complementary angles – two angles, the sum of whose measure is 90.  Supplementary angles – two angles, the sum of whose measures is 180. 1 3 2 4

7.  Vertical Angles Theorem – Vertical angles are congruent.  Congruent Supplements Theorem – If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.  Congruent Complements Theorem – If two angles are complements of congruent angles (or of the same angle, then the two angles are congruent.