Angle Proofs and Justifications

A postulate is a statement that is assumed true without proof while a theorem is a true statement that can be proven.

A theorem is a statement that is assumed true without proof while a postulate is a true statement that can be proven.

m $$\angle$$  ABD + m $$\angle$$  DBC = m $$\angle$$  ABC

1/2 $$\cdot$$  m $$\angle$$  ABC = m $$\angle$$  DBC

m $$\angle$$  ABD = m $$\angle$$  DBC

$$\angle$$  ABD $$\cong$$   $$\angle$$  DBC

Definition of supplementary

Definition of complementary

Definition of a right angle

Definition of perpendicular

$$m\angle1+m\angle2=180$$

Definition of linear pair

Linear pair postulate

definition of supplementary

$$m\angle1=180$$  Definition of straight angle

$$m\angle1=90\degree$$  Definition of perpendicular

$$m\angle1=90\degree$$  Definition of right angle

$$\angle1\ne90\degree$$  Definition of right angle

$$m\angle B=90\degree\$$  Definition of right angle

$$m\angle B=90\degree$$  Definition of perpendicular

$$\angle B\ is\ a\ right\ angle$$  Definition of perpendicular

$$\angle B\ is\ a\ right\ angle$$  Definition of right angle

Vertical Angle Theorem

Definition of Linear Pair

Addition Property

Transitive Property

Substitution Property

Definition of Linear Pair

Definition of Supplementary Angles

Angle Addition Postulate

Substitution Property

Symmetric Property

Transitive Property

Reflexive Property

Given; Definition of bisect; Transitive; Given, Definition of bisect

Given; Transitive; Given; Definition of bisect; Definition of bisect

Given; Definition of bisect; Given; Definition of bisect; Transitive