Intersecting Parallel Lines

Introduction:
The distance between the two lines are equal and they will never intersect, such lines are said to parallel lines. When a line cuts two parallel lines, it will form eight type of  angles. For intersecting parallel lines , we can also find the point of intersection distance using distance formula.

Angles of the parallel intersecting lines:

When the two parallel lines are cut by a intersecting line, then eight angles are formed. The name of angles are following

1. Corresponding angles

2. Alternate angle

• alternate interior angle
• alternate exterior angle

3.Adjacent angles

Angles in the Intersecting Parallel Lines:

Angles in intersecting parallel lines:

This diagram show intersecting parallel lines.



Angle 1 = angle 3 =angle 5=angle 7

Angle 2= angle 4 = angle 6= angle 8.

Adjacent angles:When parallel lines is cut by an intersecting line, then the adjacent angles sum up to 180 degree

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 up to 180 degree.

Corresponding angles:The angle in the same location around the intersection of two points is said to be corresponding angle.

When parallel lines are cut by an intersecting 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:When parallel lines is cut by an intersecting line, then the alternate angles are equal

So Alternate interior angle:Angle 3 = angle 5

Angle 4 = angle 6

Alternate exterior angleAngle 2 = angle 8

Angle 1 = angle 7

Examples for Intersecting Parallel Lines:

Ex 1: Find the angle 2, when the angle 1 = 100°? Use the above diagram.

Solution:Here angle 1 and 2 are adjacent angles

When parallel lines is cut by an intersecting line, then the adjacent angles sum up to 180 degree

So angle 1+angle 2 = 180

100 +angle 2= 180

Angle 2= 180-100

Angle 2 =80 degrees

Ex 2: Find the angle 4, when the angle 1 = 110°?  Use the above diagram.

Solution:Here angle 3 and 4 are adjacent angles

Angle 1= angle 3 (By vertical opposite angles are equal)

Angle 3 = 110

When parallel lines is cut by an intersecting line, then the adjacent angles sum up to 180 degree

So angle 3+ angles 4 = 180

110 +angle 4= 180

Angle 4= 180-110

Angle 4 =70 degrees.

To finding the distance between two intersecting points of parallel lines.

Ex 3: Find the distance of line intersecting two parallel lines A(1,1) B(2,2)

Solution:Formula = v(x2-x1)2 + (y2-y1)2

= v(2-1)2 + (2-1)2

= v(1) + (1)

= v2 units