3.1 Lines and Angles

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3.1 Lines and Angles

• Ms. Reser

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Standard/Objectives

• Standard 3 Students will have a foundation in
  geometric concepts.
• Objectives
• Identify relationships between lines.
• Identify angles formed by transversals.

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Homework Assignment

• Pp. 132-133 1-31

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Definitions

• Parallel lines Two lines are parallel lines if
  they are coplanar and do not intersect.
• Skew linesLines that do not intersect and are
  not coplanar.
• Parallel planestwo planes that do not intersect.

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Example 1 Identifying relationships in space

• 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
G
E
H
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Solution

1. CD, GH and EF are all parallel to AB, but only CD
   passes through D and is parallel to AB.
2. BC, AD, AE and BF are all perpendicular to AB,
   but only AD passes through D and is perpendicular
   to AB
3. DG, DH, and DE all pass through D and are skew to
   AB.
4. Only plane DCH contains D and is parallel to
   plane ABE

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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
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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
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Perpendicular Constructionpg. 130

• Use the following steps to construct a line that
  passes through a given point P and is
  perpendicular to a given line l.
• Place the compass at point P and draw an arc that
  intersects the line l twice. Label the
  intersections A and B.
• Draw an art with center A. Using the same
  radius, draw an arc with center B. Label the
  intersection of the arcs Q.
• Use a straight edge to draw PQ. PQ ? l.

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Definitions

• Transversal a line that intersects two or more
  coplanar lines at different points.

• 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

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Example 2 Identifying Angle relationships

• List all pairs of angles that fit the
  description.
• Corresponding
• Alternate exterior
• Alternate interior
• Consecutive interior

2
4
1
6
8
3
5
7
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Solution

1. ?1 and ?5 ?2 and ?6 ?3 and ?7, ?4 and ?8
2. ?1 and ?8, ?2 and ?7
3. ?3 and ?6, ?4 and ?5
4. ?3 and ?5, ?4 and ?6