Properties of the Parallel Lines

Parallel lines
          The distance between the two lines will be equal and they will never intersect, such lines are said to parallel lines.

 Properties of the parallel lines
           The parallel lines will have the same slope (m1=m2)
           Here the m1 and m2 are slopes of the lines.
           When the parallel lines are cut by transversal line, then eight angles are formed

properties :

Here
                     Angle 1 = angle 3 =angle 5=angle 7
                    Angle 2= angle 4 = angle 6= angle 8.

 Adjacent angles properties:
        when  the parallel line is cut by a transversal line, then the adjacent angles sum up to 180 degrees
                   Angle 1 +angle 2= 180 degree
                   Angle 3 +angle 4= 180 degree
                   Angle 5 +angle 6= 180 degree
                   Angle 7 +angle 8= 180 degree
                Here the adjacent angles always sum up to 180 degree.

 Corresponding angles properties
       The angle in the same position around the intersection of two points is said to be corresponding angle.
          when  the parallel line is cut by a transversal line, then corresponding angles are  equal
                    Corresponding angles:
                       Angle 1 = angle 6
                       Angle 2 = angle 5
                       Angle 3 = angle 8
                       Angle 4 =angle 7

Alternate angles properties:
                   when the parallel line is cut by a transversal line then alternate angles are equal
                   So
                    Alternate interior angle
                       Angle 3 = angle 5
                       Angle 4 = angle 6
                    Alternate exterior angle
                      Angle 2 = angle 8
                      Angle 1 = angle 7


Algebra is widely used in day to day activities watch out for my forthcoming posts on hard math problems for 8th graders and cds exam 2013. I am sure they will be helpful.

Model problems:

1.Find the angle 2, when the angle 1 = 120?
Solution:
 Here angle 1 and 2 are adjacent angles
 When parallel lines is cut by a transversal line, then the    adjacent angles sum up to 180 degree
          So angle 1+angle 2 = 180
                    120 +angle 2= 180
                     Angle 2= 180-120
                    Angle 2 =60 degrees
 2.Find the angle 4, when the angle 1 = 120?
Solution:
           Here angle 3 and 4 are adjacent angles
           Angle 1= angle 3 (vertical opposite angles are equal)
           Angle 3 = 120
 When parallel lines is cut by a transversal line, then the adjacent angles sum up to 180 degree
           So angle 3+ angles 4 = 180
                       120 +angle 4= 180
                        Angle 4= 180-120
                       Angle 4 =60 degrees.