Angles Formed by Parallel Lines Cut by a Transversal.pptx

1. Angles Formed by
Parallel Lines Cut
by a Transversal

2. Let us listen first to
the song about
Parallel Lines Cut by
a Transversal

3. In Geometry, when any two parallel
lines are cut by a transversal, many
pairs of angles are formed. This is
what we will learn in the process.
Some of them are congruent, the
others are supplementary. Let us learn
more about the angles formed when
parallel lines are cut by a transversal.

4. What are Parallel Lines Cut by Transversal?
• Parallel lines are straight equidistant lines that lie on the same plane
and never meet each other.
• When any two parallel lines are intersected by a line (known as
the transversal), the angles that are subsequently formed, have a
relationship.
• The various pairs of angles that are formed on this intersection are
Corresponding angles, Alternate Interior Angles, Alternate Exterior
Angles and Consecutive Interior Angles.
• Observe the figure given below which shows two parallel lines 'a'
and 'b' cut by a transversal 'l'.

7. Corresponding angles
When two parallel lines are intersected by a transversal, the
corresponding angles have the same relative position. In the
figure given above, the corresponding angles formed by the
intersection of the transversal are:
 ∠1 and ∠5
 ∠2 and ∠6
 ∠3 and ∠7
 ∠4 and ∠8

8. Alternate Interior Angles
Alternate interior angles are formed on the inside of two
parallel lines which are intersected by a transversal. In
the figure given above, there are two pairs of alternate
interior angles.
 ∠3 and ∠6
 ∠4 and ∠5

9. Alternate Exterior Angles
When two parallel lines are cut by a transversal, the pairs of
angles formed on either side of the transversal are named as
alternate exterior angles. In the figure given above, there
are two pairs of alternate exterior angles.
 ∠1 and ∠8
 ∠2 and ∠7

10. Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs
of angles formed on the inside of one side of the
transversal are called consecutive interior angles or co-
interior angles. In the given figure, there are two pairs of
consecutive interior angles.
 ∠4 and ∠6
 ∠3 and ∠5

11.  Example 1: Identify the corresponding angles
in the figure which shows two parallel lines 'm'
and 'n' cut by a transversal 't'.