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Basic Geometric Constructions
Copy a Segment

1) Since a segment is a part of a
   line, we’ll start by drawing a
   ray that is somewhat longer
                                          A   B
   than our intended segment,
   and call the starting point A’.




                                     A’
Copy a Segment


                                         A   B


2) Place the Needle end of the
   compass on point A, and
   adjust its length to match the
   distance AB.

                                    A’
Copy a Segment


                                        A   B




3) Without changing the width of
   the compass, put the Needle     A’       B’
   end of the compass on point
   A’, and draw the arc to cross
   your ray. Label the point of
   intersection B’. You’ve just
   copied AB to A’B’
Copy An Angle
                                          C
1) Since an angle is two rays with
   a common vertex we’ll start by
   drawing a ray and call ray
   B’A’.

                                     B
                                              A




                                     B’           A’
Copy An Angle
                                        C




2) Place the Needle end of the
                                   B
   compass on point B, and
   make an arc that crosses over            A
   from BA to BC.




                                   B’           A’
Copy An Angle
                                        C




                                   B
                                            A


3) Without changing the width of
   the compass, put the Needle
   end of the compass on point
   B’, and draw the arc crossing
   B’A’ long enough to more than
   cross where B’C’ will be.                    A’
                                   B’
Copy An Angle
4) Now go back to the original            C
   angle, and put your needle on
   the point of intersection of AB
   and the arc. Measure the
   distance along the arc to the
   ray BC.
                                     B
                                              A




                                     B’           A’
Copy An Angle
                                          C




5) Without changing the width of     B
   the compass, put your needle               A
   on the point of intersection of
   the arc and B’A’. Make an arc
   that crosses the first arc you
   drew on this new angle.




                                     B’           A’
Copy An Angle
                                          C




5) Without changing the width of     B
   the compass, put your needle               A
   on the point of intersection of
   the arc and B’A’. Make an arc
   that crosses the first arc you
   drew on this new angle.




                                     B’           A’
Copy An Angle
                                           C




                                      B
                                               A
                                               C’



6) Draw a ray from B’ thru the
   point of intersection of the two
   arcs. Label a point on the ray
   as C’. You’ve copied the angle                   A’
   ABC as A’B’C’.                     B’
Bisecting a Segment
1) Place the needle of your compass on A.
   Make its width more than half-way to B,
   and make a half-circle.




                                             A   B
Bisecting a Segment


2) Without changing the width of the
   compass, put the needle of your
   compass on B. Make a half-circle that
   overlaps the first one.                 A   B
Bisecting a Segment




                                              A   B
3) Draw a line that connects the two points
   of intersection of the two half-circles.
   That new line is both a bisector of the
   segment AB, and is perpendicular to
   AB.
Bisecting an Angle
                                                C
1) Place the needle of your compass on B.
   Draw an arc that crosses both BA and
   BC.




                                            B
                                                    A
Bisecting an Angle
                                                C
1) Place the needle of your compass on B.
   Draw an arc that crosses both BA and
   BC.




                                            B
                                                    A
Bisecting an Angle
                                                      C



                                                  E
2) Label the intersection of the arc and BA
   “D”, and the intersection of the arc and
   BC “E”.

                                              B
                                                              A
                                                          D
Bisecting an Angle
                                                     C



                                                 E



3) Place the needle of the compass on D,
   and set the width to match more than half B
   the distance to E. Make a half-circle.                    A
                                                         D
Bisecting an Angle
                                                     C



                                                 E



3) Place the needle of the compass on D,
   and set the width to match more than half B
   the distance to E. Make a half-circle.                    A
                                                         D
Bisecting an Angle
                                                     C



                                                 E




                                             B
                                                             A
                                                         D
4) Leave the compass width as it is. Place
   the needle of the compass on E, and
   make a half-circle overlapping the
   previous half-circle.
Bisecting an Angle
                                                      C



                                                  E




                                              B
                                                              A
                                                          D




5) Draw a line that connects the two points
   of intersection of the two half-circles.
   That new line is both a bisector of the
   angle ABC.

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Basicgeometricconstructions mod

  • 2. Copy a Segment 1) Since a segment is a part of a line, we’ll start by drawing a ray that is somewhat longer A B than our intended segment, and call the starting point A’. A’
  • 3. Copy a Segment A B 2) Place the Needle end of the compass on point A, and adjust its length to match the distance AB. A’
  • 4. Copy a Segment A B 3) Without changing the width of the compass, put the Needle A’ B’ end of the compass on point A’, and draw the arc to cross your ray. Label the point of intersection B’. You’ve just copied AB to A’B’
  • 5. Copy An Angle C 1) Since an angle is two rays with a common vertex we’ll start by drawing a ray and call ray B’A’. B A B’ A’
  • 6. Copy An Angle C 2) Place the Needle end of the B compass on point B, and make an arc that crosses over A from BA to BC. B’ A’
  • 7. Copy An Angle C B A 3) Without changing the width of the compass, put the Needle end of the compass on point B’, and draw the arc crossing B’A’ long enough to more than cross where B’C’ will be. A’ B’
  • 8. Copy An Angle 4) Now go back to the original C angle, and put your needle on the point of intersection of AB and the arc. Measure the distance along the arc to the ray BC. B A B’ A’
  • 9. Copy An Angle C 5) Without changing the width of B the compass, put your needle A on the point of intersection of the arc and B’A’. Make an arc that crosses the first arc you drew on this new angle. B’ A’
  • 10. Copy An Angle C 5) Without changing the width of B the compass, put your needle A on the point of intersection of the arc and B’A’. Make an arc that crosses the first arc you drew on this new angle. B’ A’
  • 11. Copy An Angle C B A C’ 6) Draw a ray from B’ thru the point of intersection of the two arcs. Label a point on the ray as C’. You’ve copied the angle A’ ABC as A’B’C’. B’
  • 12. Bisecting a Segment 1) Place the needle of your compass on A. Make its width more than half-way to B, and make a half-circle. A B
  • 13. Bisecting a Segment 2) Without changing the width of the compass, put the needle of your compass on B. Make a half-circle that overlaps the first one. A B
  • 14. Bisecting a Segment A B 3) Draw a line that connects the two points of intersection of the two half-circles. That new line is both a bisector of the segment AB, and is perpendicular to AB.
  • 15. Bisecting an Angle C 1) Place the needle of your compass on B. Draw an arc that crosses both BA and BC. B A
  • 16. Bisecting an Angle C 1) Place the needle of your compass on B. Draw an arc that crosses both BA and BC. B A
  • 17. Bisecting an Angle C E 2) Label the intersection of the arc and BA “D”, and the intersection of the arc and BC “E”. B A D
  • 18. Bisecting an Angle C E 3) Place the needle of the compass on D, and set the width to match more than half B the distance to E. Make a half-circle. A D
  • 19. Bisecting an Angle C E 3) Place the needle of the compass on D, and set the width to match more than half B the distance to E. Make a half-circle. A D
  • 20. Bisecting an Angle C E B A D 4) Leave the compass width as it is. Place the needle of the compass on E, and make a half-circle overlapping the previous half-circle.
  • 21. Bisecting an Angle C E B A D 5) Draw a line that connects the two points of intersection of the two half-circles. That new line is both a bisector of the angle ABC.