1. POSTULATES AND PROOFS
★Postulates are statements that are assumed to be true
without proof.
★ Postulates serve two purposes - to explain undefined
terms, and to serve as a starting point for proving other
statements.

2. ➣Two points determine a line segment.
Euclid of Alexandria is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements. The long lasting nature of The Elements must make Euclid the leading mathematics teacher of all time. However little is known of Euclid's life except that he taught at Alexandria in Egypt.
Euclid’s Postulates
➣Two points determine a line segment.
➣A line segment can be extended indefinitely along a line.
➣A circle can be drawn with a center and any radius.
➣All right angles are congruent.

3. Conjecture : An educated guess based on known information
Vertical Angle Conjecture : If two angles are vertical, then they are equal in measure.

4. Linear Pairs Conjecture ): Linear pairs of angles add up to 180 degrees.

5. Inductive reasoning : Examining several specific situations to arrive at a conjecture is called inductive reasoning.
If just one example contradicts the conjecture, the conjecture is not true.
The false example is called a counterexample
For example: the prime number 2 is a counterexample to the statement "All prime numbers are odd."

6. STATEMENT: A statement is any sentence that is either true or false ✧ The truth or falsity of a statement is called its truth value ✧ If the statement is represented by p then ‘not p’ is the negation of the statement and is written as ~ p ✧The truth or falsity of a statement is called its truth value.

7. A conjunction is a compound statement that is formed by joining two or more statements with the word ‘and’ or the symbol ‘^’
A disjunction is a compound statement formed by two or more statements with the word ‘or’ or the symbol ‘v’

8. Conditional statement is a statement that can be written in if-then form
The phrase immediately following the if is called the hypothesis and the word following the then is called the conclusion
Example: If you finish your homework, then you will get the points for it.

9. Deductive reasoning: Using facts, rules, definitions, or properties to reach logical conclusions is termed as deductive reasoning

10. Once a statement or conjecture has been proven to be true, it is called a ‘Theorem’
A short proof that relies heavily on given theorem is called a ‘corollary’
Examples: Theorem: Supplements of congruent angles are congruent.
Corollary: Supplements of the same angle are congruent.