math 7 geometry 04 angles, parallel lines, and transversals - grade 7
TRANSCRIPT
A Mathematics 7 Lecture
Next Century Mathematics: The New Grade 7
Angles and
Parallel Lines
Parallel Lines: A Review
Definition: Two lines are parallel if they lie on the same plane but do not intersect.
m
n
Line m is parallel to line n
Symbol: m || n
Angles and Parallel Lines
Transversal
Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
tm
n
Line t is a transversal
Angles and Parallel Lines
Transversal
When a transversal t intersects line n and m, eight angles of the following types are formed:
Exterior angles
Interior angles
Vertical Angles
Linear Pairs
Alternative exterior angles
Alternative interior angles
Corresponding angles
tm
n
Angles and Parallel Lines
Angles and Parallel Lines
t
m
n
We’ll consider the angles formed by a pair of parallel lines cut by a transversal and their properties.
When a transversal tintersects parallel line n and m, eight angles of the following types are formed:
Vertical Angles
Linear Pairs
Corresponding angles
Alternate exterior angles
Alternate interior angles
Consecutive interior angles
Consecutive exterior angles
Angles and Parallel Lines
If two parallel lines are cut
by a transversal, then the
following pairs of angles are
congruent:
1. Vertical Angles
2. Corresponding angles
3. Alternate interior angles
4. Alternate exterior angles
Angles and Parallel Lines
t
m
n
Angles and Parallel Lines
Vertical Angles
Vertical Angles:
1 4, 2 3, 5 8, 6 7
Two angles that are opposite angles.
Vertical angles are congruent.
1 2
3 4
5 6
7 8
Vertical angles are
congruent
Angles and Parallel Lines
Corresponding Angles
Corresponding Angles: Two angles that occupy
corresponding positions.
2 6, 1 5, 3 7, 4 8
1 2
3 4
5 6
7 8
Corresponding
angles are
congruent
Angles and Parallel Lines
Alternate Angles
Alternate Interior Angles: Two angles that lie between
parallel lines on opposite sides of the transversal but are
not a linear pair
3 6, 4 5
1 2
3 4
5 6
7 8
Alternate interior
angles are
congruent
Angles and Parallel Lines
Alternate Exterior Angles
Alternate Exterior Angles: Two angles that lie outside
parallel lines on opposite sides of the transversal.
2 7, 1 8
1 2
3 4
5 6
7 8
Alternate exterior
angles are
congruent
Angles and Parallel Lines
If two parallel lines are cut by
a transversal, then the
following pairs of angles are
supplementary:
1. Adjacent angles
2. Consecutive interior angles
3. Consecutive exterior angles
Angles and Parallel Lines
t
m
n
Angles and Parallel Lines
Adjacent Angles
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5
Adjacent angles form linear pairs; i.e., they form a
180 angle
1 2
3 4
5 6
7 8
Adjacent angles
are
supplementary
Angles and Parallel Lines
Consecutive Angles
Consecutive Interior Angles: Two angles that lie
between parallel lines on the same sides of the
transversal.
m3 +m5 = 180º, m4 +m6 = 180º
1 2
3 4
5 6
7 8
Angles and Parallel Lines
Consecutive
interior angles are
supplementary
Consecutive Angles
Consecutive Exterior Angles: Two angles that
lie outside parallel lines on the same sides of
the transversal.
m1 +m7 = 180º, m2 +m8 = 180º
1 2
3 4
5 6
7 8
Angles and Parallel Lines
Consecutive
exterior angles
are
supplementary
Example 1: In the figure, line AB is parallel to
line CD and s is a transversal.
g h
fe
ac
db
s
DC
BA
a. Give all pairs of
angles falling under
the following:
vertical,
corresponding,
alternate interior,
alternate exterior,
adjacent
Examples
Angles and Parallel Lines
Example 1: Answerg h
fe
ac
db
s
DC
BA
Examples
Angles and Parallel Lines
Vertical CorrespondingAlternate
interior
Alternate
exteriorAdjacent
Example 1: In the figure, line AB is parallel to
line CD and s is a transversal.
g h
fe
ac
db
s
DC
BA
b. If ma = 100, find
the measures of all
the other angles
Examples
Angles and Parallel Lines
100
Example 1b: If ma = 100, here are the
measures of the other angles:
g h
fe
ac
db
s
DC
BA
Examples
Angles and Parallel Lines
100
100
80
80
100 80
80 100
Thank
you!