**Important Concepts and Formulas**

1. If a ray stands on a line, then the
sum of the two adjacent angles so formed is 180° and vice-versa. This property is
called as the linear pair axiom.

2. If two lines intersect each other,
then the vertically opposite angles are equal.

3. If a transversal intersects two
parallel lines, then

i.
each
pair of corresponding angles is equal.

ii.
each
pair of alternate interior angles is equal.

iii.
each
pair of interior angles on the same side of the transversal is supplementary.

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4. If a transversal intersects two lines
such that, either

i.
any
one pair of corresponding angles is equal, or

ii.
any
one pair of alternate interior angles is equal, or

iii.
any
one pair of interior angles on the same side of the transversal is
supplementary, then the lines are parallel.

5. Lines which are parallel to a given
line are parallel to each other.

6. The sum of the three angles of a
triangle is 180°.

7. If a side of a triangle is produced,
the exterior angle so formed is equal to the sum of the two interior opposite
angles.

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