** CHAPTER 6 LINES AND ANGLES**

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__Line segment__: A line segment is a line with two end points.

__Ray__: A part of the line with one end point is called a ray.

__Collinear points__: If three or more points lie on the same line, they are called collinear points

__Non-collinear points__: If three or more points do not lie on the same line they are said to be non-collinear.

__Angle__: An angle is formed when two rays originate from the same end point.

__Arms__: The arms of an angle are the rays that make the angle.

__Vertex:__ The end point at which the rays making the angle meet is called the vertex.

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TYPES OF ANGLE:

__Acute angle__: An angle measuring between 0^{o} and 90^{o} is an acute angle.

__Right angle:__ An angle equal to 90^{o} is called a right angle.

__Obtuse angle__: An angle measuring greater than 90^{o}but less than 180^{o} is called an obtuse angle.

__Reflex angle__: An angle measuring greater than 180^{0} but less than 360^{0} is called a reflex angle.

__Complementary angles__: Two angles whose sum is 90^{o} are called complementary angles.

__Supplementary angles__: Two angles whose sum is 180^{o} are called supplementary angles.

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AXIOMS AND THEOREMS

Linear pair axioms:

Axiom 1: If a ray stands on a line, then the sum of two adjacent angles so formed is 180^{o}.

Axiom 2: If the sum of two adjacent angles is 180^{o}, then the non-common arms of the angles form a line.

Corresponding angles axiom:

Axiom 3: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

Axiom 4: If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.

Theorems:

- If two lines intersect each other, then the vertically opposite angles are equal.
- If a transversal intersects two lines, then each pair of alternate interior angles is equal.
- If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
- If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
- If a transversal intersects two lines such that a pair of interior angles are on the same side of the transversal is supplementary, then the two lines are parallel.
- Lines which are parallel to the same line are parallel to each other.
- The sum of the angles of a triangle is 180
^{o}. - If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.