Post on 17-Dec-2015
transcript
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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 -
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
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, 2, 7, 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, 4, 5, 6
Parallel Lines and Transversals
Identifying Angles -
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.
Parallel Lines and Transversals
Identifying Angles -
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.
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
and
or
and
Alternate interior angles are congruent.
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
and
or
and
Alternate exterior angles are congruent.
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
and
and
and or
and
Corresponding angles are congruent.
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.
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.
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.
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.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
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.