parallel lines and transversals geometry d – section 3.1

Parallel Lines and Transversals

Geometry D – Section 3.1

A

B

DC


What would you call two lines which do not intersect?

Parallel

A solid arrow placed on two lines of a diagram indicate the lines are parallel.

The symbol || is used to indicate parallel lines.

AB || CD


A slash through the parallel symbol || indicates the lines are not parallel.

AB || CD

AD

B

C


Transversal -

When two parallel lines are cut by another line this is called a transversal.

t

mkj Parallel lines t and s are intersected by line j, k and m. Therefore, line j, k and m are a transversal of lines t and s.

S


Identifying Angles -

t

kj

1

23

45

67

8

Exterior angles are on the exterior of the two lines cut by the transversal.

The exterior angles are:

1, 2, 7, 8



t

kj

1

23

45

67

8

Interior angles are on the interior of the two lines cut by the transversal.

The interior angles are:

3, 4, 5, 6



Vertical angles are:

When two lines intersect they form two pairs of “opposite” angles called vertical angles.

< 1 and < 3

< 2 and < 4

Vertical angles are congruent.

Congruent means angles with the same measurement.



If the sum of the measures of two angles is 90° the angles are complementary.

Angles a and b are complementary.

If the sum of the measures of two angles is 180°, they are supplementary.

Angles a and b are supplementary.



t

kj

1

23

45

67

8

Alternate interior angles are on the interior of the two lines and on opposite sides of the transversal.

Alternate interior angles are:

3 6,

4 5

and

or

and

Alternate interior angles are congruent.



t

kj

1

23

45

67

8

Alternate exterior angles are on the exterior of the two lines and on opposite sides of the transversal.

Alternate exterior angles are:

1 8,

2 7

and

or

and

Alternate exterior angles are congruent.



t

kj

1

23

45

67

8

Corresponding angles are on the corresponding side of the two lines and on the same side of the transversal.

Corresponding angles are:1 5,

3 7,

2 6,

4 8

and

and

and or

and

Corresponding angles are congruent.

http://www.mrperezonlinemathtutor.com/G/1_2_Angles_in_Parallel_lines.html

2. 2 and 10 are alternate interior angles.


Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

Determine if the statement is true or false. If false, correct the statement.

1. Line r is a transversal of lines p and q.

True – Line r intersects both lines in a plane.

False - The angles are corresponding angles on transversal p.

4. 1 and 15 are alternate exterior angles.




1 2 3 4

5678

9 10 11 12

13141516


False – The angles are vertical angles created by the intersection of q and r.

True - The angles are alternate exterior angles on transversal p.

6. 10 and 15 are vertical angles.




1 2 3 4

5678

9 10 11 12

13141516


True – The angles are alternate interior angles on transversal q.

False- 10 and 16 are vertical angles

Determine if the statement is true or false. If false, correct the statement. 7. 3 and 4 are

alternate exterior angles.

8. 16 and 14 are corresponding angles.



1 2 3 4

5678

9 10 11 12

13141516

False – The angles are a linear pair, they are supplementary angles.

True – The angles are corresponding on transversal s.

http://www.mathopenref.com/anglesalternateinterior.html

parallel lines and transversals geometry d – section 3.1

Documents

angles vertical angles

corresponding angles

alternate interior angles

alternate exterior angles

parallel lines t

congruent means angles

pairs of opposite angles

transversal of lines