GEOMETRIC CONSTRUCTIONS

1
GEOMETRIC CONSTRUCTIONS

• Create geometric figures using only a compass and
  a straightedge (no protractors or rulers
  allowed).
• (Never erase the marks you make with your
  compass, THAT IS YOUR WORK!)

Melancolia, Albrecht Durer, 1514
2
School of Athens, Raphael, 1509-1510
3
Construction Copy a Segment

1. Draw a ray.
2. Open your compass so that it touches the two
   endpoints of the segment.
3. Now place your compass at the endpoint of your
   ray and draw an arc that intersects the ray.
4. Mark the intersection as the second endpoint of
   the segment.

4
Construction Copy an Angle

• Draw an arc centered at the vertex.
• Now draw the same arc on a ray which will be one
  side of your copied angle. Make sure it
  intersects the ray.
• At the original angle, adjust your compass to the
  distance between the two points where the first
  arc intersected the sides of the angle.
• Using this measurement, place your compass at the
  point of intersection created in Step 2. Now
  draw an arc passing through the first arc.
• Connect the vertex and the pt. of intersection of
  the two arcs, and you should have a copy of the
  angle.
• How would you make a copy of a segment? Give it
  a try.

5
Construction Equilateral Triangle

• Think of the Flower of Life
• Draw a segment.
• Draw two arcs the length of the segment, one from
  each endpoint.
• Mark where the arcs intersect, and connect this
  point to the two endpoints of your original
  segment.
• Used to construct a 60? angle

6
Construction Bisecting an Angle

• Draw an arc of any measure with its center at the
  vertex of the angle. Make sure the arcs
  intersects both sides of the angle.
• Place your compass tip on one of the intersection
  points and draw an arc.
• Draw the same size arc on the other point of
  intersection.
• Connect the vertex of the angle to the
  intersection of the two arcs you just drew.
• How would you use this construction to
  construct a 30? angle? Now try this.
• Try and construct all the angle bisectors of a
  triangle.

7
Example Proving ASA Using Constructions

• Construct triangle ABC given two angles and their
  included side.