Constructions Mira/Compass and Straightedge/Computer
Activity Directions
1. Complete each construction three times:
(1) Mira,
(2) compass and straightedge,
(3) Computer dynamic geometry software
(Wingeom, NonEuclid, or Geometer's Sketchpad)
2. For each construction, write step by step directions on how to make the
construction.
3. For each construction, write an outline for proving the construction is valid.
Follow up Questions
1. What are the advantages to using
(1) Mira,
(2) compass and straightedge,
(3) computer dynamic geometry software?
2. What are the disadvantages to using
(1) Mira,
(2) compass and straightedge,
(3) computer dynamic geometry software?
Constructions Mira/Compass and Straightedge/Computer
Construction 1: Given a segment, construct a segment congruent to the given segment.
Construction 2: Given a segment, construct the perpendicular bisector of the segment.
Construction 3: Given a segment, construct the midpoint.
Construction 4: Given a point on a line, construct the perpendicular to the line at the
given point.
Construction 5: Given a line and a point not on the line, construct the line perpendicular
to the line through the given point.
Construction 6: Given an angle, construct an angle congruent to the given angle.
Construction 7: Given an angle, construct the bisector of the angle.
Construction 8: Given a line and a point not on the line, construct the line parallel to the
given line through the given point.
Application 1
1. Given a triangle, construct the bisector of each angle.Drag the vertices of the
triangle to change its shape and size.
What do you observe happens with the three angle bisectors?
2. Construct a perpendicular segment from the intersection point to each side of the
triangle. Measure the length of each segment. Drag the vertices of the triangle to
change its shape and size.
What do you observe about the three lengths?
3. Construct a circle with the center at the point of intersection of the angle bisectors
to a point where a perpendicular segment is on the triangle. Drag the vertices of
the triangle to change its shape and size.
What do you observe about the circle?
Teacher Notes
My personal philosophy is that basic constructions should be done with physical tools
such as Mira or compass and straightedge. A calculator or computer should be used for
only two situations: (1) for more complex constructions where the error from so many
steps becomes so great that the final construction is not close to the theoretical
construction, and (2) for exploration or investigation.