# CLASS-8GEOMETRY-PROPERTIES OF PARALLEL LINES

Properties of Parallel Lines -

Let the transversal EF intersect two parallel lines AB and CD at the points L and M respectively. Then the following properties hold –

Property.1)

Each pair of corresponding angles are equal

In the figure, ∠1 = ∠5 and ∠2 = ∠6, ∠3 = ∠7 and ∠4 = ∠8

Property.2)

Each pair of alternate angles are equal

In the figure, ∠1 = ∠7 and ∠2 = ∠8

Property.3)

The interior angles on the same side of the transversal (also called co-interior angles) are supplementary.

In the figure, ∠1 + ∠8 = 180⁰  and  ∠2 + ∠7 = 180⁰

Property.1)

Lines which are paralleled to the same line are parallel to each other.

If AB || EF and  CD || EF then AB || CD

Property.2)

If two lines are parallel, a line perpendicular to one of them is also perpendicular to the other.

If AB || CD  and  EF ⊥ AB  then  EF ⊥  CD

Property.3)

The distance between two parallel lines is constant.

If AB || CD and PQ and RS are perpendiculars to both AB & CD then PQ = RS.

Conditions of Parallelism

If a transversal intersects two straight lines such that –

1) The corresponding angles are equal, or

2) The alternate angles are equal, or

3) The co-interior angles are supplementary than the two lines are parallel to each other.