The Intersection
Constructor: To construct the intersection of two geometric
objects, first select the objects. If an intersection can be
constructed for the selected objects, the intersection button will be
enabled. Clicking the mouse
on this button will plot the point of intersection of the two
objects. (example)
The Midpoint Constructor:
Select any segment or segments. Once a segment has been selected,
the midpoint
constructor button will be enabled, and clicking on it will plot the
midpoint
of the selected segment. If you select more than one segment, this
button
will plot the midpoints of each of the selected segments. (example)
The Perpendicular
Line Constructor: Two selections must be made for this particular
construction
to occur: a line (or segment or ray) and a point. Once this is
done, the perpendicular line button
will be enabled, and clicking on it will construct a line through the
selected
point which is perpendicular to the selected object. (example)
The Parallel
Line Constructor: This construction is quite similar to the
perpendicular
line construction. A line (or segment or ray) and a point must be
selected. Once this is done, the parallel line
constructor button will be enabled, and clicking on it will construct a
line
through the selected point which is parallel to the selected line,
segment,
or ray. (Note: In the Poincare model, two ultraparallels will be
constructed, and in Elliptic Geometry, no parallels are possible)
(example)
The Segment
Constructor: If you have two points on the canvas, you can
construct
a segment using those two points. After selecting both of the
points, the segment
constructor button in the Tool Panel will be enabled. Clicking the
mouse
on this button will construct a segment connecting the two selected
points.
The Circle
Constructor: Circles can be constructed using this button in three
different ways. Either select the desired center point of the
circle and then
a point which is to be on the circle, or select the desired center
point
and then a segment which is the appropriate radius length, or select
three
points, all of which are desired to be located on the circle's
circumference.
Once one of these selections has been made, the circle constructor will
become enabled, and clicking on it will construct a circle. (Note: In
Hyperbolic and Elliptic Geometry, only the first two options
apply) (example)
The Filled
Circle/Arc Constructor: Once you have selected a circle or an arc,
the filled circle/arc constructor button will be enabled.
Clicking on this
button will fill in the interior of the circle/arc. If you select
more
than one circle/arc, the filled circle constructor will fill every
circle/arc
that has been selected. (example)
The Arc Constructor:
Arcs can be constructed using this button in three different
ways. Either select
the desired center point of the arc and then a point which is to be on
the arc, or select two points that are attached to a circle, or select
three
points, all of which are desired to be located on the arc's
circumference.
Once one of these selections has been made, the arc constructor will
become
enabled, and clicking on it will construct the desired arc. In
the first option a dialog
box will pop up asking for the initial and terminal angles of the arc
(in
degrees). (Note: In Hyperbolic and Elliptic Geometry, only the first
two options apply)
(example)
The Open Polygon
Constructor: Select each of the points
that you would like to be a vertex in the open polygon (three or more
points
are necessary). Once this selction has been made, the open
polygon tool will be enabled. Clicking on this button will result
in a polygon that has its first vertex the first point selected, the
second vertex the second point selected, and so on. If you first
select a set of
points using the box selection method, the order of connection of the
selected
points in the polygonm that is constructed is the order in which the
points were originally created.
The Closed
Polygon Constructor: As in constructing an open polygon, selecting
the points that you would like to be vertices is the first step in
constructing
a closed polygon. After doing so, the closed polygon button will be
enabled.
The only difference between the closed polygon and the open polygon
constructors
is that the closed polygon constructor constructs a segment between the
last
point selected and the first point selected, thereby closing the
figure.
The Filled
Polygon Constructor: The construction of a filled polygon is much
like the construction of an open or closed polygon. After
selecting
the points you would like as vertices, the filled polygon constructor
button
will be enabled. Clicking on this button will result in the
construction of an area that fills
the interior of the polygon with the current default color. You
can select a
filled polygon by clicking anywhere in the interior of the polygon (of
course while using the selection arrow from the tool panel). (example)
The Angle Bisector
Constructor: To construct an angle bisector, first select
three points which define an angle. The first point you click on will
be considered to be a point
on the initial ray of the angle. The second point will be considered to
be the vertex of the angle. The third point will be a point on the
terminal
ray of the angle. Upon clicking the angle bisector button, a ray will
be constructed that bisects the defined angle. The angle bisector
construction is
oriented, which means that if you select the points in reverse order, a
ray will be drawn in the opposite direction. (example)
The Locus Menu: At the top of the Construct Panel there
is a pop-up menu labeled "Locus". A locus construction
depends
on two objects: 1) a point that is attached to a one-dimensional object
(line,ray,segment,circle,or arc) and 2) any other geometric object
(called
the "locus primitive".) The locus of the primitive will be a set of
copies
of that primitive as the attached point moves along its one-dimensional
path. (example)