Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Β
Math 7 geometry 04 angles, parallel lines, and transversals - grade 7
1.
2. A Mathematics 7 Lecture
Next Century Mathematics: The New Grade 7
Angles and
Parallel Lines
3. 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
4. Transversal
Definition: A line that intersects two or more
lines in a plane at different points is called a
transversal.
t
m
n
Line t is a
transversal
Angles and Parallel Lines
5. 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
t
m
n
Angles and Parallel Lines
6. Angles and Parallel Lines
t
m
n
Weβll consider the angles
formed by a pair of
parallel lines cut by a
transversal and their
properties.
When a transversal t
intersects parallel line n and
m, eight angles of the
following types are formed:
οΆ Vertical Angles
οΆ Linear Pairs
οΆ Corresponding angles
οΆ Alternate exterior angles
οΆ Alternate interior angles
οΆ Consecutive interior
angles
οΆ Consecutive exterior
angles
Angles and Parallel Lines
7. 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
8. Vertical Angles
Vertical Angles:
ο 1 ο ο 4, ο 2 ο ο 3, ο 5 ο ο 8, ο 6 ο ο 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
10. Alternate Angles
Alternate Interior Angles: Two angles that lie between
parallel lines on opposite sides of the transversal but are
not a linear pair
ο 3 ο ο 6, ο 4 ο ο 5
1 2
3 4
5 6
7 8
Alternate interior
angles are
congruent
Angles and Parallel Lines
11. Alternate Exterior Angles
Alternate Exterior Angles: Two angles that lie outside
parallel lines on opposite sides of the transversal.
ο 2 ο ο 7, ο 1 ο ο 8
1 2
3 4
5 6
7 8
Alternate exterior
angles are
congruent
Angles and Parallel Lines
12. 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
13. Adjacent Angles
ο1 & ο2 , ο2 & ο4 , ο4 &ο3, ο3 & ο1,
ο5 & ο6, ο6 & ο8, ο8 & ο7, ο7 & ο5
Adjacent angles form linear pairs; i.e., they form a
180ο° angle
1 2
3 4
5 6
7 8
Adjacent angles
are
supplementary
Angles and Parallel Lines
14. Consecutive Angles
Consecutive Interior Angles: Two angles that lie
between parallel lines on the same sides of the
transversal.
mο3 +mο5 = 180ΒΊ, mο4 +mο6 = 180ΒΊ
1 2
3 4
5 6
7 8
Angles and Parallel Lines
Consecutive
interior angles are
supplementary
15. Consecutive Angles
Consecutive Exterior Angles: Two angles that
lie outside parallel lines on the same sides of
the transversal.
mο1 +mο7 = 180ΒΊ, mο2 +mο8 = 180ΒΊ
1 2
3 4
5 6
7 8
Angles and Parallel Lines
Consecutive
exterior angles
are
supplementary
16. 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
17. Example 1: Answer
g h
fe
ac
db
s
DC
BA
Examples
Angles and Parallel Lines
Vertical Corresponding
Alternate
interior
Alternate
exterior
Adjacent
18. 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 mοa = 100ο°, find
the measures of all
the other angles
Examples
Angles and Parallel Lines
100ο°
19. Example 1b: If mοa = 100ο°, here are the
measures of the other angles:
g h
fe
ac
db
s
DC
BA
Examples
Angles and Parallel Lines
100ο°
100ο°
80ο°
80ο°
100ο° 80ο°
80ο° 100ο°