Geometric Constructions

Jason Wofsey, May 13, 2016

Automatic Checking geometric constructions.

Table of Contents

  1. Basic Constructions
    1. Congruent Segment Construction
    2. Perpendicular Bisector Construction
    3. Angle Bisector Construction
    4. Perpendicular Through Point on Line
    5. Perpendicular Line through Point
    6. Congruent Angle Construction
    7. Parallel Line Construction
    8. Blank Construction
    9. Angle 45° Construction
    10. Angle 135° Construction
    11. Angle 22.5° Construction
  2. Polygon Constructions
    1. Equilateral Triangle Construction
    2. Rhombus Construction from Segment
    3. Square Construction from Segment
    4. Rectangle Construction
    5. Regular Hexagon Construction
    6. Parallelogram Construction from Sides and Angle
  3. Conics Constructions
    1. Parabola Construction
    2. Circle Through Point 1
    3. Circle Center Construction
  4. Transformations
    1. Reflection Construction
    2. Translation Construction

1.

Basic Constructions

  • 1. Congruent Segment Construction
  • 2. Perpendicular Bisector Construction
  • 3. Angle Bisector Construction
  • 4. Perpendicular Through Point on Line
  • 5. Perpendicular Line through Point
  • 6. Congruent Angle Construction
  • 7. Parallel Line Construction
  • 8. Blank Construction
  • 9. Angle 45° Construction
  • 10. Angle 135° Construction
  • 11. Angle 22.5° Construction

1.1.

Congruent Segment Construction

Construct a segment on the green ray with endpoint C that is congruent to segment AB.
– Jason Wofsey

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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2.

Polygon Constructions

  • 1. Equilateral Triangle Construction
  • 2. Rhombus Construction from Segment
  • 3. Square Construction from Segment
  • 4. Rectangle Construction
  • 5. Regular Hexagon Construction
  • 6. Parallelogram Construction from Sides and Angle

2.1.

Equilateral Triangle Construction

Construct an Equilateral Triangle with side AB
– Jason Wofsey

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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3.

Conics Constructions

  • 1. Parabola Construction
  • 2. Circle Through Point 1
  • 3. Circle Center Construction

3.1.

Parabola Construction

Find a point that is equidistant from the given line and point A.
– Jason Wofsey

3.2.

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3.3.

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4.

Transformations

  • 1. Reflection Construction
  • 2. Translation Construction

4.1.

Reflection Construction

Reflect triangle ABC about line DE.
– Jason Wofsey

4.2.

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Information