Introduction of Lines And Angles

Definitions :

1. Point: Any line segment whose length is zero units is called a point.

2. Line: A line which has no ends points and it is denoted by AB

3. Ray: Any line which has one end point is called a ray and its denoted by

    AB or BA

4. Line segment: Any line which has two end points is called a line segment

        and its denoted as by AB or BA.

5. Angle: When a ray is rotated on anti-clock wise direction, then the space

   which is obtained between the initial and the final ray is called a

   ray angle.

 Note:

 * An angle has two arms

 * An angles has a vector

 Types of Angles:

1. Zero angle: An angle whose measurement is 0 is called zero angle

2. Acute angle: An angle whose measurement is more than 0° and less than

     90° is called acute angle.

3. Right angle: An angle whose measurement is exactly 90° is called a right

    angle.

4. Obtuse Angle: An angle whose measurement is more than 90° and less

        than 180° is called obtuse angle.

5. Reflex angle: A angle whose measurement is more than 180° and less

     than 360° is called reflex angle.

6. Complete Angle: A angle whose measurement is exactly 360° is called

             complete angle

     Ex: 30°, 60° .... etc.

7. Straight angle: An angle whose measurement is exactly 180° is called

         straight angle.

8. Complementary angles: Two angle are said to be complementry angles if

        their sum is 90°

     Ex: 30°, 60° and 45°, 45° ...... etc.

9. Supplementary Angles : Two angles are said to be supplementary angle if

       their sum is 180°.

       Ex: 100° and 80°, 10° and 170° ........ etc.

10. Adjacent Angles : Two adjacent angles are said to be adjacent angles if

       they have a common vertex and common arm.

11. Linear Pair Property : The sum of the linear pair of angles is

       supplementary.

12. Exterior Angle Property : Each exterior angle of an angle is equal to the

       same sum of the opposite interior angles.

13. Transversal : A line which intersects two parallel lines at two distinct

       points is called a transversal.

 Note :

* If line intersects two parallel lines, then

 (a) 4 pair of corresponding angles are formed i.e. ∠1 and ∠5.

 (b) 4 pair of corresponding angles are formed (i.e 2 points of alternate

  interior, 2 pairs of alternate exterior) i.e. ∠1 and ∠7, ∠2 and ∠4, ∠3

  and ∠5, ∠4 and ∠6.

 (c) 4 pairs of angles on the same side of the transversal are formed (2

  points of interior, 2 pairs of exterior) i.e. ∠1 and ∠8, ∠2 and ∠8, ∠3

  and ∠6, ∠4 and ∠5.

 (d) Corresponding angles are equal, i.e. ∠1=∠5; ∠2=∠6, ∠3=∠7 and

  ∠4=∠8.

 (e) Alternate angles are equals i.e. ∠1=∠7; ∠2=∠8, ∠3=∠5 and ∠4=∠6.

 (f) Sum of interior and exterior angles on the same side of the transversal

  is equal to 180° i.e. ∠1-∠8=180°; ∠2-∠7 180°; ∠6 180° and ∠4-∠5

  180°.

 (g) If one pair of corresponding angles are equal or one pair of alternate

  angles are equal, then the two given lines are always parallel to each

  other.

 (h) If the sum of one pair of interior angles on the same side of the

  transversal or exterior angles on the same side of the transversal is

  equal to 180° (supplementary) then the two given lines are parallel

  to each other.

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