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Middle/High School Algebra, Geometry, and Statistics (AGS)
5.12 Important Points

1. Axioms: Axioms are self-evident truths or basic facts formed as a result of observation and intuition.

2. Theorems: New relations derived with the help of undefined terms, defined terms and axioms are called theorems.

3. Proof is a chain of steps leading to the conclusion.

There are two types of proof which are mostly used.

(i)Direct Proof: We start with hypothesis and derive the conclusion through a chain of conditionals. Most of the theorems are proved through this method.

(ii)Indirect Proof: In this method we assume that the conclusion is false and proceed as in the direct method. At one stage we arrive at a mathematical absurdity. So we conclude that our assumption is false and so the given conclusion is true.

4. A line is a set of infinite number of points. If a number of points lie on the same line they are called collinear points, lines in the same plane are called coplanar lines.

5. If a transversal intersects a pair of parallel lines, then,
(i) The alternate angles are equal.
(ii) The corresponding angles are equal.
(iii) The interior angles on the same side of the transversal are supplementary.

6. If two lines are parallel to the same line, they are parallel to each other.

7. If two lines are perpendicular to each other, they are parallel to each other.