Perform basic constructions'

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Chapter 10

• Perform basic constructions.
• Sate and apply the theorems involving concurrent
  lines.
• Describe the locus that satisfies a basic
  condition.

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Lecture 1 (10-1, 10-2)

• Objectives
• Perform your first few constructions.

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Constructions

• An accurate drawing that fits a set of conditions
  and uses only a straightedge and a compass and
  obeys all the rule of geometry.

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Construction 1
Given a segment, construct a congruent
segment. Given Construct Steps
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Construction 2
Given an angle, construct a congruent
angle. Given Construct Steps
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Construction 3
Given an angle, construct the bisector of the
angle Given Construct Steps
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Construction 4
Given a segment, construct the perpendicular
bisector of the segment. Given Construct Steps
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Construction 5
Given a point on a line, construct the
perpendicular to the line through the
point. Given Construct Steps
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Construction 6
Given a point outside a line, construct the
perpendicular to the line through the
point. Given Construct Steps
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Construction 7
Given a point outside a line, construct a line
parallel to the given line through the
point. Given Construct Steps
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Lecture 2 (10-3, 10-4, 10-5)

• Objectives
• Learn your next few constructions.

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Theorem 10-1
The bisectors of the angles of a triangle meet at
a point that is equidistant from the sides of the
triangle.
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Theorem 10-2
The perpendicular bisectors of the sides of a
triangle intersect in a point equidistant from
the vertices of the triangle.
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Theorem 10-3
The lines that contain the altitudes of a
triangle intersect in a point.
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Theorem 10-4
The medians of a triangle intersect in a point
that divides their lengths into segments with a
12 ratio.
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Construction 8
Given a point on a circle, construct the tangent
to the circle through the point. Given Construct
Steps
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Construction 9
Given a point outside a circle, construct the
tangent to the circle through the
point. Given Construct Steps
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Construction 10
Given a triangle, circumscribe a circle about the
triangle. Given Construct Steps
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Construction 11
Given a triangle, inscribe a circle within the
triangle. Given Construct Steps
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Construction 12
Given a segment, divide the segment into a given
number of congruent segments. Given Construct S
teps
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Construction 13
Given three segments, construct a fourth segment
so that the four segments are proportional. Given
Construct Steps
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Construction 14
Given two segments, construct their geometric
mean. Given Construct Steps
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Lecture 3 (10-6, 10-7)

• Objectives
• Define a locus
• Describe a locus that satisfies a given condition.

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Locus

• The set of all points that satisfy a condition or
  set of conditions.

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Example

• Describe the set of all points in a plane
  equidistant from a given point, C.

Circle C
C
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Example

• Describe all the points in a plane that are
  equidistant from points A and B.

Perpendicular bisector of AB
A
B
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Lecture 4 (10-8)

• Objectives
• Use construction techniques to describe and solve
  locus problems.

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Example

• Determine the locus of the points points in a
  plane that are 1.5 in from X and 1 in from line m.

X
m
Sketch
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Focal Point 4

• Are you a leader or a follower?
• Do you try to blend in with the crowd, or stand
  apart?
• The choices you make now will affect not only
  your morals, but your opportunities in the
  future.
• Choose carefully.