**Parallel lines **are those which do not meet any were in the plane when extended infinitely.

The distance between the parallel lines is always the same.

Real Life Examples: The railway track, opposite edges of computer monitor, opposite edges of the rectangular table.

In the above diagram, the line l is parallel to m, in symbol we denote $l\parallel m$.

**Transversal: **If a line intersects two or more parallel lines at distinct points, then it is called a transversal.

### Parallel lines and angles

In the above diagram, the transversal t, intersects the parallel lines at, P. Q and R.

**Angles made by a transversal with the pair of parallel lines.**In the above diagram, we can see that the transversal t cuts the parallel lines m and n.

The 8 angles formed are named as, $\angle 1$, $\angle 3$, $\angle 2$, $\angle 4$, $\angle 5$, $\angle 7$, $\angle 8$

We can classify these angles into the following pairs of angles with their respective properties.

**1. ****Vertically opposite angles:** Pair of vertically opposite angles are equal.

$\angle 1$ = $\angle 3$

$\angle 2$ = $\angle 4$

$\angle 5$ = $\angle 7$

$\angle 8$ = $\angle 8$

**2. ****Linear Pair:**$\angle 1$ + $\angle 2$ = 180

^{o } ,

^{ } $\angle 5$ + $\angle 6$ = 180

^{o } $\angle 2$ + $\angle 3$ = 180

^{o } , $\angle 6$ + $\angle 7$ = 180

^{ o } $\angle 3$ + $\angle 4$ = 180

^{ o } , $\angle 7$ + $\angle 8$ = 180

^{ o } $\angle 4$ + $\angle 1$ = 180

^{o } , $\angle 8$ + $\angle 5$ = 180

^{ o } **3. ****Corresponding Angles:** Pair of corresponding angles are equal.

$\angle 1$ = $\angle 5$

$\angle 2$ = $\angle 6$

$\angle 3$ = $\angle 7$

$\angle 4$ = $\angle 8$

**4. Alternate Interior angles:** Pair of alternate interior angles are equal.

$\angle 3$ = $\angle 5$

$\angle 4$ = $\angle 6$

**5. Alternate Exterior angles:** Pair of alternate exterior angles are equal.

$\angle 2$ = $\angle 8$

$\angle 7$ = $\angle 7$

**6. ****Co-interior angles:** Pair of co-interior angles are supplementary. These angles are also called as consecutive interior angles.

$\angle 3$ + $\angle 6$ = 180

^{ o} $\angle 4$ + $\angle 5$ = 180

^{ o} ### Solved Example

**Question: **Find the measure of the angle x in the following diagram.

** Solution: **

In the above diagram, $GE\parallel AB$.

Therefore, $\angle GEA$ = $\angle EAB$ [ alternate interior angles ]

=> $\angle GEA$ = 40 ^{o} ----------------( 1 )

Moreover, $GE\parallel CD$.

Therefore, $\angle GEC$ = $\angle ECD$ [ alternate interior angles ]

=> $\angle GEC$ = 110 ^{o} -------------------( 2 )

But $\angle GEC$ = $\angle GEA$ + $\angle AEG$

= 40 + x --------------------( 3 )

Therefore 40 + x = 110 [ equating ( 2 ) and ( 3 ) ]

=> x = 110 - 40

= 70 ^{o}