1. Properties of Transversal Lines

2. Introduction
Lines:
Line is a straight path and extends in both directions without end. A B l
A line through two points A and B can be written as
Also it is denoted by l
Since line does not have end points we cannot find its length
The following are not lines since they does not have straight path.
AB or BA

3. l3 l1 l2 AB or BA CD or DC EF or FE
Example:- Identify the lines from the figure A B C D E F l1 l2 l3
We can see 3 lines from the figure,
Line l1 or
Line l2 or
Line l3 or
AB or BA
CD or DC
EF or FE

4. Line segment is a line that ends at both side.
We use capital letter to denote end of line segment.
In the above figure the line segment has two end point A and B.
A line segment with end points A and B is written as
Since line segment has end points, we can measure its lengths
AB or BA

5. AB or BA BD or DB CD or DC CA or AC
Example :- Identify the line segment from the figure A B C D
We can see 4 line segments from the figure,
Line
AB or BA
BD or DB
CD or DC
CA or AC

6. Parallel lines
Two lines that go on forever on either side without meeting each other are called parallel lines.
Lines l1 and l2 are parallel lines
Lines l3 and l4 are parallel lines
Lines l5 and l6 are parallel lines l3 l4 l5 l6 l1 l2

7. Transversal lines
A straight line intersects two or more given lines at distinct points is called a
transversal to the given lines. The given lines may or may not be parallel.
Transversal Lines
Transversal Lines
Transversal Lines
Transversal Lines

8. Transversal lines 3 5 2 1 4 6 7 8 A B C D X YM N
In the given figure a pair of lines
AB and CD
are cut by a transversal
XY ,
intersecting the
two lines at points M and N respectively.
The points M and N are called points of intersection.
When a transversal intersects two lines the eight angles marked 1 to 8 have their
special names. Let us see what those angles are

9. ∠3 , ∠4, ∠5 and ∠6 are interior angles
When two parallel lines are crossed by another line (which is called the
Transversal), an Interior Angle is the pair of angles on the inner side of each of
those two lines. 4 3 6 5
∠3 , ∠4, ∠5 and ∠6 are interior angles

10. Exterior angles
When two parallel lines are crossed by another line (called the Transversal),
Exterior Angles are a pair of angles on the outer side of each of those two lines 2 1 7 8
∠1 , ∠2, ∠7 and ∠8 are exterior angles.

11. Corresponding angles
When two parallel lines are crossed by another line (which is called the
Transversal), the angles in matching corners are called corresponding angles. 2 6 1 5
∠1 and ∠5 ,
∠2 and ∠6 ,
∠3 and ∠7 ,
∠4 and ∠8
are pairs of corresponding angles 8 4 3 7

12. Interior alternate angles
When two parallel lines are crossed by another line (called the Transversal),
Interior alternate angles are a pair of angles on the inner side of each of
those two lines but on opposite sides of the transversal. 4 6 3 5
∠3 and ∠5 , ∠4 and ∠6 are the pairs of interior alternate angles

13. Exterior alternate angles
When two parallel lines are crossed by another line (called the Transversal),
Exterior alternate angles are a pair of angles on the outer side of each of
those two lines but on opposite sides of the transversal. 2 8 1 7
∠1 and ∠7, ∠2 and ∠8 are the pairs of exterior alternate angles

14. Interior angles on same side of transversal
When two parallel lines are crossed by another line (called the Transversal),
The following pairs of angles are interior angles on same side of transveral 4 5 3 6
∠3 and ∠6, ∠4 and ∠5 are the pairs of Interior angles
on same side of transversal

15. Exterior angle on same side of transversal
When two parallel lines are crossed by another line (called the Transversal),
The following pairs of angles are exterior angles on same side of transveral 1 8 2 7
∠1 and ∠8, ∠2 and ∠7 are the pairs of exterior angle
on same side of transversal

16. Vertically opposite angles
Angles opposite to each other when two lines cross are called vertical opposite angles. 2 4 1 3
∠1 and ∠3 ,
∠2 and ∠4 ,
∠5 and ∠7 ,
∠6 and ∠8
are pairs of vertical angles 5 7 6 8

17. Adjacent Supplementary angles
Adjacent supplementary angles are adjacent angles on the same side of the transversal 1 2 3 2 3 4 1 4 5 6 7 6 7 8 5 8
∠1 and ∠2 , ∠2 and ∠3 , ∠3 and ∠4 , ∠4 and ∠1, ∠5 and ∠6, ∠6 and ∠7, ∠7 and ∠8,
∠8 and ∠5 are pairs of adjacent supplementary angles.

18. Name of all angles formed when a transversal intersects two lines are as follows
Interior angles
∠3 , ∠4, ∠5 and ∠6
Interior alternate angles
∠3 and ∠5 , ∠4 and ∠6 3 5 2 1 4 6 7 8
Exterior angles
∠1 , ∠2, ∠7 and ∠8
Exterior alternate angles
∠1 and ∠7, ∠2 and ∠8
Corresponding angles
∠1 and ∠5 , ∠2 and ∠6 ,
∠3 and ∠7 , ∠4 and ∠8
Vertical angles
∠1 and ∠3 ,∠2 and ∠4 ,
∠5 and ∠7 ,∠6 and ∠8
Adjacent Supplementary angles
∠1 and ∠2 , ∠2 and ∠3 , ∠3 and ∠4 , ∠4 and ∠1, ∠5 and ∠6, ∠6 and ∠7, ∠7 and ∠8, ∠8 and ∠5

19. Try These In the given figure identify, Pairs of Interior angles
Pairs of Interior alternate angles
Pairs of Exterior angles
Pairs of Exterior alternate angles
Pairs of Corresponding angles
Vertically opposite angles
Adjacent supplemetary angles