LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

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.**