Properties of Transversal Lines

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

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

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

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

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

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

Transversal lines 3 5 2 1 4 6 7 8 A B C D X Y M 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

∠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

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.

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

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

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

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

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

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

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.

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

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