History of geometric constructions

1

• History of geometric constructions
• Develop skill using a compass, straightedge, and
  modern tools
• Expand your skills to make more complex figures
• Apply construction skills to learn some facts
  about triangles

2
Duplicating Segments and Angles

• Euclid, a mathematician who lived in ancient
  Greece, is considered the father of geometry.
• Much of the early work in geometry was performed
  using a compass and straightedge.
• Euclid used these tools in writing his famous
  book Elements.

3
Duplicating Segments and Angles

• Geometric figures can be created in three ways
• A sketch is done freehand
• A drawing is done using a ruler and protractor
• A construction is done using a compass and
  straightedge
• This chapter will focus on using a compass and
  straightedge to construct geometric figures.

4
Duplicating Segments and Angles

• When doing a construction, a compass is used to
  create circles and copy distances.
• If you use a ruler as a straightedge, you must
  ignore all measurement markings on it.
• Remember to mark your figure as needed to
  indicate perpendicular or parallel lines and
  congruent segments or angles.

5
Duplicating Segments and Angles

• Investigation 1
• Constructing the duplicate of a segment
• Stage 1
• Draw segment AB and a ray with endpoint C
• Point C will be one endpoint of the duplicate
• Stage 2
• Take your compass and open it up so that the
  pointer is at A and the pencil tip is at B
• Stage 3
• Without opening or closing the compass, place
  the pointer at C and draw a small arc on the ray
• The point where the arc crosses the ray is point D

6
Duplicating Segments and Angles

• Investigation 2
• Constructing the duplicate of an angle
• Stage 1
• Draw angle DEF and a ray with endpoint G
• Point G will be the vertex of the duplicate
• Stage 2
• Place your compass pointer at E and sweep an arc
  that crosses both sides of the angle
• Copy that arc to the ray as shown
• Stage 3
• Place your compass pointer at the point where the
  arc crosses the side of the angle and adjust the
  compass to draw a small arc as shown
• Make a copy of the arc from the point where the
  first arc crosses ray G
• Draw the other side of the angle from point G
  through the point where the two arcs cross