Segments, Rays, and Lines

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Segments, Rays, and Lines

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Segments, rays, and lines are fundamental objects in Euclidean geometry. In classical geometry constructions, you use a straightedge to construct these objects.

An axis acts as a line for most purposes.

A straight object is a path object.

You can change the object properties, label properties, and display attributes of straight objects.


Construct a Straight Object

Sketchpad provides several ways to construct straight objects.

Use a Straightedge tool to construct a straight object based on two points.Use existing points, create new independent points, or create points on paths or intersections.

Constrain the straight object to be horizontal, vertical, or at other common angles by pressing and holding the Shift key while you drag.

Use the Construct | Segment, Construct | Ray, or Construct | Line command to construct a straight object using two selected points.

Use the Construct | Perpendicular Line or Construct | Parallel Line command to construct a line parallel or perpendicular to a selected straight object.

Use the Construct | Angle Bisector command to construct the ray bisecting the angle formed by three selected points.

Use a Straight Object

Construct a point on a straight object using the Point tool or the Construct | Point on Object command. Then animate the point along the straight object or use the point as the driver for a locus.

Attach an independent point to the straight object by using the Edit | Merge command.

Use a straight object as a mirror for reflections by choosing the Transform | Mark Mirror command.

Use Construct | Midpoint to construct a segment’s midpoint.

Use Construct | Intersection to construct a straight object’s intersection with another straight object, a circle, an arc, a point locus, or a function plot.

Use Construct | First Intersection to construct a ray’s first intersection with a polygon. (The first intersection is the intersection closest to the ray's endpoint.)

Use Graph | Define Unit Distance to define a coordinate system with a unit distance defined by one or two selected segments. (The unit of the coordinate system is defined by the length of the segment.)

If you use two selected segments, the first defines the unit for x, and the second for y.

Measure a Straight Object

Use the Measure menu to find:

the Length of a segment

the Ratio of two segments’ lengths

the Equation of a line

the Slope of any straight object