Postulates
A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. A postulate is that elementary statement which we have to assume while making a demonstration.
Postulate is a true statement, which does not require to be proved.
Examples:
- A straight line may be drawn from one point to any other point in the same plane.
- We can produce a finite straight line to any length in a straight line in either direction.
- We can cut off a straight line of any length from a given straight line either from it or by producing it.
- The magnitude of an angle does not depend upon the length of its arms.
More About Postulate
- Postulate is used to derive the other logical statements to solve a problem.
- Postulates are also called as axioms.
Example:
To prove that these triangles are congruent, we use SSS postulate, as the corresponding sides of both the triangles are equal.
Example:
Ques: State the postulate or theorem you would use to prove that ∠1 and ∠2 are congruent.
Choices:
A. corresponding angles postulate
B. converse of corresponding angles postulate
C. alternate angles are congruent
D. adjacent angles are congruent
Correct Answer: A
Solution:
Step 1:∠1 and ∠2 corresponding angles.
Step 2: Since the lines a and b are parallel, ∠1 and ∠2 are congruent. [Corresponding angles postulate.]
Step 3: So, corresponding angles postulate is used to prove that ∠1 and ∠2 are congruent.