G-CO.12 Geometric Constructions

Claire Verti, Feb 1, 2018

G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines; including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Table of Contents

  1. Familiarity with GeoGebra tools
    1. Learning how to use GeoGebra for Constructions.
    2. G-CO.12 Construction #2. Copying an Angle.
    3. G-CO.12 Construction #3 Bisecting a segment
    4. G-CO.12 Construction #4 Bisecting an Angle
    5. G-CO.12 Construction #5 Constructing Perpendicular Lines
    6. G-CO.12 Construction #6 Perpendicular bisector of a line segment
    7. G-CO.12 Construction #7 Constructing a line parallel to a given line through a point not on the line
  2. G-CO.12 The Seven Constructions
    1. G-CO.12 Construction #1. Copying a segment.

1.

Familiarity with GeoGebra tools

This digital worksheet will help familiarize students with the various tools within GeoGebra.

  • 1. Learning how to use GeoGebra for Constructions.
  • 2. G-CO.12 Construction #2. Copying an Angle.
  • 3. G-CO.12 Construction #3 Bisecting a segment
  • 4. G-CO.12 Construction #4 Bisecting an Angle
  • 5. G-CO.12 Construction #5 Constructing Perpendicular Lines
  • 6. G-CO.12 Construction #6 Perpendicular bisector of a line segment
  • 7. G-CO.12 Construction #7 Constructing a line parallel to a given line through a point not on the line

1.1.

Learning how to use GeoGebra for Constructions.

Geometric Constructions using a compass and a straightedge.
1. Place three non-collinear points on your screen.[br]2. Turn the labels on so that you can see the names of the points.[br]3. Draw ray AB, and ray AC.[br]4. Place your compass at point A so that it passes through point C and the arc intersects ray BC.[br]5. Use the intersect feature to create the intersection point. [br]6. Turn the labels on for all the intersection points.[br]7. Place your compass at another point on the figure to draw another circle.[br]8. Create and label all the new intersection points.
– Claire Verti

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2.

G-CO.12 The Seven Constructions

  • 1. G-CO.12 Construction #1. Copying a segment.

2.1.

G-CO.12 Construction #1. Copying a segment.

Steps.
1. Place two points on the screen. point A and [br]point B.[br]2. Connect the two points, A and B, with a "segment".[br]3. Place 1 point on the screen, but not on the segment. point C.[br]4. "Measure" the initial segment AB using a compass.[br]5. Place the compass on C and "click" the point.[br]6. Place a new point anywhere on the circle. point D.[br]7. Connect the two points with a "segment". Line segment CD.
To name a point, right-click on the point after it has been place, and select "show label".
What is true about line segment AB and line segment CD? How do you know?
– Claire Verti

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