complimentary angles, supplementary angles, and parallel lines
TRANSCRIPT
Complimentary Angles, Supplementary Angles, and
Parallel Lines
Adjacent angles are “side by side” and share a common ray.
45º15º
These are examples of adjacent angles.
55º
35º
50º130º
80º 45º
85º20º
These angles are NOT adjacent.
45º55º
50º100º
35º
35º
When 2 lines intersect, they make vertical angles.
75º
75º
105º105º
Vertical angles are opposite one another.
75º
75º
105º105º
Vertical angles are congruent (equal).
30º150º
150º30º
Supplementary angles add up to 180º.
60º120º
40º
140º
Adjacent and Supplementary Angles
Supplementary Anglesbut not Adjacent
Complementary angles add up to 90º.
60º
30º40º
50º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
Parallel Lines and PlanesParallel Lines and Planes
You will learn to describe relationships among lines, parts of lines, and planes.
In geometry, two lines in a plane that are always the same distance apart are ____________.parallel lines
No two parallel lines intersect, no matter how far you extend them.
Parallel Lines and PlanesParallel Lines and Planes
Definition of
Parallel
Lines
Two lines are parallel if they are in the same plane and do not ________.intersect
Parallel Lines and TransversalsParallel Lines and Transversals
In geometry, a line, line segment, or ray that intersects two or more lines atdifferent points is called a __________transversal
l
m
B
A
AB is an example of a transversal. It intercepts lines l and m.
Note all of the different angles formed at the points of intersection.
1 2
34
5
76
8
Parallel Lines and TransversalsParallel Lines and Transversals
Definition of
Transversal
In a plane, a line is a transversal if it intersects two or more
lines, each at a different point.
The lines cut by a transversal may or may not be parallel.
l
m
1 2
34
576
8
ml
Parallel Lines
t is a transversal for l and m.
t
1 234
5
7
6
8
b
c
cb ||
Nonparallel Lines
r is a transversal for b and c.
r
Parallel Lines and TransversalsParallel Lines and Transversals
Two lines divide the plane into three regions.
The region between the lines is referred to as the interior.
The two regions not between the lines is referred to as the exterior.
Exterior
Exterior
Interior
l
m
1 2
34
576
8
Parallel Lines and TransversalsParallel Lines and Transversals
When a transversal intersects two lines, _____ angles are formed.eight
These angles are given special names.
t
Interior angles lie between thetwo lines.
Exterior angles lie outside thetwo lines.
Alternate Interior angles are on the opposite sides of the transversal.
Consecutive Interior angles are on the same side of the transversal.
Alternate Exterior angles areon the opposite sides of thetransversal.
Parallel Lines and TransversalsParallel Lines and Transversals
Theorem 4-1
Alternate
Interior
Angles
If two parallel lines are cut by a transversal, then each pair of
alternate interior angles is _________.
1 234
57
68
64 53
congruent
Parallel Lines and TransversalsParallel Lines and Transversals
1 2
34
576
8
Theorem 4-2
Consecutive
Interior
Angles
If two parallel lines are cut by a transversal, then each pair of
consecutive interior angles is _____________.supplementary
18054 18063
Parallel Lines and TransversalsParallel Lines and Transversals
1 2
34
576
8
Theorem 4-3
Alternate
Exterior
Angles
If two parallel lines are cut by a transversal, then each pair of
alternate exterior angles is _________.congruent
71 82
Transversals and Corresponding AnglesTransversals and Corresponding Angles
l
m
1 2
34
576
8
t
When a transversal crosses two lines, the intersection creates a number ofangles that are related to each other.
Note 1 and 5 below. Although one is an exterior angle and the other is an interior angle, both lie on the same side of the transversal.
Angle 1 and 5 are called __________________.corresponding angles
Give three other pairs of corresponding angles that are formed:
4 and 8 3 and 7 2 and 6
Transversals and Corresponding AnglesTransversals and Corresponding Angles
Postulate 4-1
Corresponding
Angles
If two parallel lines are cut by a transversal, then each pair of
corresponding angles are _________.congruent
Transversals and Corresponding AnglesTransversals and Corresponding Angles
Concept
Summary
Congruent Supplementary
alternate interior
alternate exterior
corresponding
consecutive interior
Types of angle pairs formed when a transversal cuts two parallel lines.
Transversals and Corresponding AnglesTransversals and Corresponding Angles
s t
c
d
1 2 3 45 6 7 8
9 10 11 12
13 14 15 16
s || t and c || d.
Name all the angles that arecongruent to 1.Give a reason for each answer.
3 1 corresponding angles
6 1 vertical angles
8 1 alternate exterior angles
9 1 corresponding angles
11 9 1 corresponding angles
14 1 alternate exterior angles
16 14 1 corresponding angles