Download 3.1 Notes

Geometry
Unless you try to do
something beyond
what you have
already mastered,
you will never grow.
Ralph Waldo Emerson
Today:
• Chapter 2 Check
• 3.1 Instruction
• Practice
Warm Up
How many degrees are in a triangle?
What is the relationship between these 2
angles?
Name the relationship between
1 and 2.
1
2
You used angle and line segment relationships
to prove theorems.
• Identify relationships between two lines or
two planes.
• Name angle pairs formed by parallel lines
and transversals.
Content Standards
G.CO.1 Know precise definitions of angle, circle,
perpendicular line, parallel line, and line
segment, based on the undefined notions of
point, line, distance along a line, and distance
around a circular arc.
Mathematical Practices
1 Make sense of problems and persevere in
solving them.
3 Construct viable arguments and critique the
reasoning of others.
3.1 Lines and Angles
Objectives:
1. Identify the relationships of lines
2. Identify angles formed by transversals
Vocabulary:
Parallel, perpendicular, skew, transversal,
corresponding angles, alternate exterior angles,
alternate interior angles, consecutive interior
angles
3.1 Lines and Angles
Vocabulary:
Parallel:
Parallel Planes:
Real Life Ex:
Parallel Lines:
Real Life Ex:
3.1 Lines and Angles
Vocabulary:
Perpendicular:
Real Life Ex:
Transversal:
Real Life Ex:
Skew:
Real Life Ex:
Which line is a transversal?
n
1 2
4 3
5 6
8 7
Angle Types:
Interior: 3, 4, 5, 6
Exterior: 1, 2, 7, 8
b
a
3.1 Lines and Angles
Corresponding Angles: angles that occupy
corresponding position. Same side of transversal,
one on the interior and one on the exterior.
1 22
44 33
55
88
66
77
Examples: <1 and < 5, <2 and <6, <3 and <7, <4 and <8
3.1 Lines and Angles
Alternate Exterior Angles: angles on opposite sides
of the transversal that are both exterior
1 2
4 3
5 6
88 77
Examples: <1 and <7, <2 and <8
3.1 Lines and Angles
Alternate Interior Angles: angles on opposite sides
of the transversal that are both interior
1 2
44 33
5 66
8 7
Examples: <3 and <5, <4 and <6
3.1 Lines and Angles
Consecutive Interior Angles: angles on the same
side of the transversal, both interior
1 2
44 33
5 6
8 7
Examples: <3 and <6, <4 and <5
Find:
a
Alternate interior angles
b
1
2
4
3
9 10
12 11
5
6
8
Need to focus on one
transversal at a time!!!!!
7
c
<3 and <9,
<4 and <10
Find:
a
Alternate interior angles
b
1
2
4
3
9 10
12 11
5
NEXT TRANSVERSAL!
6
8
7
c
<3 and <6,
<2 and <5
Find:
a
Alternate interior angles
b
1
2
4
3
9 10
12 11
<5 and <11,
<8 and <10
5
LAST TRANSVERSAL!
6
8
7
c
Find:
a
Alternate interior angles
b
Total:
<3 and <9,
<4 and <10,
<3 and <6,
<2 and <5,
<5 and <11,
<8 and <10
1
2
4
3
9 10
12 11
5
6
8
7
c
Geometry
Unless you try to do
something beyond
what you have
already mastered,
you will never grow.
Ralph Waldo Emerson
Assignment:
•
3.1 p. 175 #1-3, 9-12, 55