PARALLEL LINES

PARALLEL LINES

1. If two lines in a plane do not intersect each other they are called parallel lines Example - Railway lines, opposite edges of text books.

   • IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN THE
     • • pairs of corresponding angles are equal
       • Pairs of alternate ( interior as well as exterior) angles are equal.
         • Interior angles on the same side of the transversal are supplementary.
   • IF A TRANSVERSAL CUTS A PAIR OF THE LINES IN SUCH A WAY THAT -
     • The angles of any pair of corresponding angles are equal, or
       • The angles of any pair of alternate interior ( or exterior) angles are equal, or
         • The angles of any pair of interior angles on the same side of transversal are supplementary.
           • DISTANCE BETWEEN PARALLEL LINES
             • THE METHOD FOR CALCULATING THE DISTANCE BETWEEN PARALLEL LINES
               • Ensure whether the equations of the given parallel lines are in slope- intercept form.
                 • The intercepts (c¹ and c²) and slope value which is common for both the line has to be determined.
                   • After obtaining the above values, substitute them in the slope - intercept equation to find y.
                     • Finally put all the above values in the distance formula to find the distance between two parallel lines.
                       • LINES PARALLEL TO A GIVEN LINE.
                         • Lines parallel to a given line in a plane are parallel to each other.
                           • Example Find the slope of the line parallel to the line. 4x -5y=12 . To find these we need to get the line into slope intercept form which means we need to solve for y. The slope of the line 4x -5y=12 is m =4/5.
                             • Two lines in the same plane perpendicular to a given line are parallel to each other.
                               • DIVISION OF A LINE SEGMENT INTO EQUAL PARTS
                                 • The division of line segments is defined as a line that can be divided into n number of equal parts.
                                   • Here we will divide a line segment of 15 cm in the ratio of 2:1 as,
                                     • Let us take CB =x, then AC will be 2x .
                                       • AC+CB =2x+x=15, x=5 AC =10 cm CB = 5cm .
                                         • DIVISION OF A LINE SEGMENT IN A GIVEN RATIO INTERNALLY.
                                           • Let (x¹, y¹) and (x², y²) be the cartesian co- ordinatebaxes OX and OY and the point R divides the line segment PQ internally in a given ratio m:n (say) i.e. PR :RQ =m:n.