PARALLEL LINES Maths Geoemtry

 

PARALLEL LINES

       If  two lines not having any common point on the same plane  then these lines are called Parallel Lines.

       The angle between two parallel line is 0^0  or 〖180〗^0

       Lines which do not intersect are called Parallel lines.

       The relation is parallel to is denoted by the symbol "∥" and is read as is parallel to.

       If two lines are drawn in  plane such that they do not intersect, even when extended is definitely in both the directions, then such lines are called parallel lines.

       If lines l and m are parallel, we show them by marking arrows on the lines pointing in the same directions  and we write, l∥m read as  ‘ l is parallel to m’.

       The perpendicular distance between two parallel lines is the same every where.

v Two lines are parallel if

The lines lie on the same plane and they do not intersect.

       Two lines are parallel to the given line are parallel to each other.

       Two lines are perpendicular to the same line, then they are parallel to each other.

       TRANSVERSAL: A line which intersects two distinct lines in a plane in exactly two points, is called  transversal.

       A line which intersects two or more given  lines in a plane at different  points is called a transversal to the given lines.

       When a transversal cuts two lines, 8 angles are formed.

This is because at each intersection 4 angles are formed.

Corresponding Angles:

Two angles are said to be a pair of corresponding angles.  If

i.          They are on the same side of the transversal

ii.          One is an interior angle and the other is an exterior angle

iii.          They are not adjacent angles.

Alternate Interior Angles:Two angles are said to be a pair of alternate interior  angles.

If      i)            Both are interior angles

ii)                They are on either side of the transversal.

iii)            They are not adjacent angles.

Alternate Exterior Angles:Two angles are said to be a pair of alternate exterior  angles.  If   i)  Both are exterior angles

i.          They are on either side of the transversal.

ii.      They are not adjacent angles.               

Co interior angles:-   Two angles are interior and one side of the transversal

Co exterior angles:-  Two angles are exterior and one side of the transversal.

       When a transversal intersects two parallel lines, then

       Pairs of interior alternate angles are equal          .

       Pairs of exterior alternate angles are equal

       Pairs of corresponding  angles are equal

       The sum of the interior or exterior angles on the same  side of the transversal is  

       Pairs of  co-interior angles are supplementary.