Transcript 3.1 Lines and Angles Mrs. Spitz Fall 2004 Standard/Objectives: Standard 3: Students will have a foundation in geometric concepts. Objectives: • Identify relationships between lines. • Identify.

3.1 Lines and Angles
Mrs. Spitz
Fall 2004
Standard/Objectives:
Standard 3: Students will have a
foundation in geometric concepts.
Objectives:
• Identify relationships between lines.
• Identify angles formed by transversals.
Homework Assignment
• Pp. 132-133 #1-31
Definitions
• Parallel lines – Two lines are parallel
lines if they are coplanar and do not
intersect.
• Skew lines—Lines that do not intersect
and are not coplanar.
• Parallel planes—two planes that do not
intersect.
Example 1: Identifying
relationships in space
•
a.
b.
c.
d.
Think of each segment in
the diagram. Which
appear to fit the
description?
Parallel to AB and contains
D
Perpendicular to AB and
contains D
Skew to AB and contains D
Name the plane(s) that
contains D and appear to
be parallel to plane ABE
B
C
D
A
F
E
G
H
Solution
CD, GH and EF are all parallel to AB, but
only CD passes through D and is parallel to
AB.
b. BC, AD, AE and BF are all perpendicular to
AB, but only AD passes through D and is
perpendicular to AB
c. DG, DH, and DE all pass through D and are
skew to AB.
d. Only plane DCH contains D and is parallel to
plane ABE
a.
Postulate 13: Parallel Postulate
• If there is a line and a point not on the
line, then there is exactly one line
through the point parallel to the given
line.
P
l
Postulate 14: Perpendicular
Postulate
• If there is a line and a point not on the
line, then there is exactly one line
through the given point perpendicular
to the given line.
P
l
Perpendicular Construction—pg.
130
Use the following steps to construct a line
that passes through a given point P and is
perpendicular to a given line l.
1. Place the compass at point P and draw an
arc that intersects the line l twice. Label
the intersections A and B.
2. Draw an art with center A. Using the same
radius, draw an arc with center B. Label
the intersection of the arcs Q.
3. Use a straight edge to draw PQ. PQ  l.
•
Definitions:
• Transversal: a line that
intersects two or more
coplanar lines at
different points.
1
2
3 4
5 6
7 8
• Angles 1 and 5 are
corresponding angles
• Angles 1 and 8 are
alternate exterior angles
• Angles 3 and 5 are
alternate interior
angles.
• 3 and 5 are consecutive
interior angles
Example 2: Identifying Angle
relationships
•
a.
b.
c.
d.
List all pairs of
angles that fit the
description.
Corresponding
Alternate exterior
Alternate interior
Consecutive
interior
2
4
1
3
6
5
8
7
Solution:
a. 1 and 5; 2 and 6; 3 and 7,
4
b. 1
c. 3
d. 3
and
and
and
and
8
8, 2 and 7
6, 4 and 5
5, 4 and 6