Theorems on Angle Pairs
Along with postulates and definitions, the structure of geometry also includes a logical chain of statements called theorems. A theorem is a statement that still needs to be proven by means of definitions, postulates, algebraic properties, and rules of logic.
Definition
A theorem is a statement that can be proven. A corollary of a theorem is a statement that can be easily proven using the theorem.
There are theorems on angle pairs that you can easily prove. In the activity below, you can formulate a conjecture using inductive reasoning. Then use deductive reasoning to prove your conjecture. Note that a conjecture becomes a theorem if proven.
Activity
- Draw two angles that are supplementary and congruent. Name them and
- Find and
- Classify and
Conjecture:
If two angles are supplementary and congruent, then each is a _______________.
A direct two-column proof of this conjecture is shown in the next page. Because such conjecture can be proven, it can already be considered as a theorem.
