parallel lines with transversals
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Parallel Lines and Transversals
A
B
DC
Parallel Lines and Transversals
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
Parallel Lines and Transversals
A slash through the parallel symbol || indicates the lines are not parallel.
AB || CD
AD
B
C
Parallel Lines and Transversals
Transversal -A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel.
t
mkj
Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.
Parallel Lines and Transversals
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, <7, <2, <8
Parallel Lines and Transversals
Identifying Angles -
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, <5, <4, <6
Parallel Lines and Transversals
Identifying Angles -
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
Parallel Lines and Transversals
Identifying Angles -
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
Parallel Lines and Transversals
Identifying Angles -
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
2. < 2 and < 10 are alternate interior angles.
Parallel Lines and Transversals
∠
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.
2. < 2 and < 10 are alternate interior angles.
Parallel Lines and Transversals
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.
3. <3 and < 5 are alternate interior angles.
Parallel Lines and Transversals
∠
∠
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.
∠
∠
4. < 1 and < 15 are alternate exterior angles.
3. < 3 and < 5 are alternate interior angles.
Parallel Lines and Transversals
∠
∠
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.
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 < 11 are consecutive interior angles.
5. < 6 and < 12 are alternate interior angles.
Parallel Lines and Transversals
∠
∠
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.
∠
∠
6. < 10 and < 11 are consecutive interior angles.
5. < 6 and < 12 are alternate interior angles.
Parallel Lines and Transversals
∠
∠
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.
True – The angles are alternate interior angles on transversal q.
∠
True – The angles are consecutive interior angles on transversal s.
∠
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.
Parallel Lines and Transversals
∠
∠
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. 7. < 3 and < 4 are alternate
exterior angles.
8. < 16 and < 14 are corresponding angles.
Parallel Lines and Transversals
∠
∠
Identifying Angles – Check for Understanding
1 2 3 4
5678
9 10 11 12
13141516
∠
∠
False– The angles are adjacent angles on transversal r.
True – The angles are corresponding angles on transversal s.