and a Transversal Vocabulary Parallel lines Lines in the same plane that have the same slope and never intersect Transversal A line that intersects two or more parallel lines Interior Angles ID: 533524
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Slide1
Parallel Lines
and a TransversalSlide2
Vocabulary
Parallel lines
: Lines in the same plane that have the same slope and never intersect.
Transversal
: A line that intersects two or more parallel lines.Slide3
Interior Angles
: Angles that lie between the parallel lines.
Same Side Interior Angles
: Interior angles on the same side of the transversal. Alternate Interior Angles: Angles that lie between the parallel lines and on opposite sides of the transversal, and are congruent.
VocabularySlide4
Exterior Angles
: Angles that lie outside the parallel lines.
Same Side Exterior Angles
: Exterior angles on the same side of the transversal. Alternate Exterior Angles: Angles that lie outside the parallel lines and on opposite sides of the transversal, and are congruent.
VocabularySlide5
Corresponding Angles
: Angles that are in the same relative position and are congruent.
Supplementary Angles
: Angles that have a sum of 180.Linear Pair: Two angles with a common side that are supplementary.
Vertical Angles
: Formed when two lines cross, they are on opposite sides of both lines.
VocabularySlide6
Theorem
When
parallel lines
are cut by a transversal, then the pairs of corresponding angles are
congruent
, the pairs of
alternate interior angles
are
congruent
, and the pairs of
alternate exterior angles
are
congruent
.Slide7
Converse of the Theorem
When
corresponding
angles
or
alternate
interior angles or
alternate
exterior angles
are
con
gru
ent
, then
the lines that are cut
by
the
transversal
to form the angles are
parallel
. Slide8
Corresponding Angles
Observe where the angles from the top intersection end up when it is “cut out” and slid down the transversal…Slide9
Identifying Angles.
In the figure below,
, and
is a transversal.
Parallel lines:
Transversal:
Interior Angles:
Exterior Angles:
Corresponding Angles:
Alt. Int. Angles
:
Alt. Ext. Angles:
Supplementary:
Vertical Angles:
Linear Pairs: Slide10
Discussion
Consider the relationships between the angles…
How many angles do we need to know the measure of in order to determine the measure of the rest?
How many different angle measures should we expect to see amongst the angles?
1
2Slide11
What if…
What if
L
1 and L
2
were not parallel?
Which angles are corresponding angles? Are they congruent? Why or why not?
L
1
L
2
m
1
2
3
4
5
6
7
8Slide12
Example 1
1. If
is
k
parallel to
l?
Be prepared to
Explain
.
16
15
14
13
12
11
10
9
7
6
5
4
3
2
1
8
2. If
is
m
parallel to
n
?
Be prepared to
Explain
.
y: yes n: no
y: yes n: noSlide13
Example 2
16
15
14
13
12
11
10
9
7
6
5
4
3
2
1
8
Using the diagram below, determine if angles 1 and 9 are: a) interior b) exterior c) vertical d) correspondingSlide14
Example 3
16
15
14
13
12
11
10
9
7
6
5
4
3
2
1
8
Using the diagram below, determine if angles 10 and 15 are:
a) Alternate Interior b) Alternate Exterior c) Vertical d) CorrespondingSlide15
Example 4
Using the diagram below, determine if angles 1 and 4 are: a) interior b) exterior c) vertical d) corresponding
16
15
14
13
12
11
10
9
7
6
5
4
3
2
1
8Slide16
Example 5
16
15
14
13
12
11
10
9
7
6
5
4
3
2
1
8
Using the diagram below, determine if angles 5 and 2 are: a) interior b) exterior c) vertical d) corresponding