**Parallel
Lines and Transversal**

Parallel
lines are lines which extend in the same direction and remain the same distance
apart.

In the
following figure, AB and CD are parallel lines. We denote them by “AB // CD”
and say “AB is parallel to CD”.

The rails on
railway track are parallel.

In geometry,
parallel lines are indicated with equal numbers of arrow heads on each line.

**Transversal**

When a line
intersects two other lines, the line is called a

**transversal**of those two lines. In the figure, there are 8 angles formed at the two intersections where TS cuts lines AB and CD.
These angles are named in pairs according to
their relative positions as follows:

1. ∠a
and ∠p,
∠b
and ∠q,
∠c
and ∠r,
∠d
and ∠s
are pairs of corresponding angles.

**Conditions When Parallel Lines are Cut by a Transversal**

When two parallel lines are cut by a transversal, then

1. their corresponding angles are equal,

2. their alternate angles are equal,

3. their consecutive interior angles are supplementary.

The converse statements for the above are also true. That is, when two
straight lines AB and CD are cut by a transversal TS, then

1. if the corresponding angles are equal, then AB // CD,

2. if the alternate angles are equal, then AB // CD,

3. if the consecutive interior angles are supplementary, then AB // CD.

**Example 1:**In the figure, AB // CD. Find the measures of angles x, y and z.

**Solution:**∠x = 70° (corr. ∠s, AB // CD)

∠y = 70° (alt. ∠s, AB // CD)

∠z + 70° = 180° (int. ∠s, AB // CD)

∴ ∠z = 110°

**Example 2:**In the figure, BA // DE. Find the measure of angle x.

**Solution:**Construct FC // BA // DE.

∠x

_{1}= 35° (alt. ∠s, FC // DE)
∠x

_{2}= 30° (alt. ∠s, FC // BA)
∠x = ∠x

_{1}+ ∠x_{2}
= 35° + 30°

= 65°