Geometry Explorer Help

The Tool Panel:

Construct Sub-Panel:

(Help Main Page)

intersect 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)

midpoint 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)

perpendicular 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)

parallel 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)

segment by two points 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.

circle by two 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)

filled circle/arc 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)

arc1 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)

open polygon 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.

closed polygon 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.

filled polygon 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)

angle bisector 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)