CLASS-8
GEOMETRY-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
Additional properties of parallel lines
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.