Describe Geometry Construction Set

In GeoCnstr, you draw:

• line segments
• rectangles
• squares
• triangles
• circles

Then, view information, e.g., perimeter, area, or perform operations, e.g., inscribe circle, bisect side.

Keywords: education, learning, geometry, construction

Use GeoCnstr

Tap i:Help to view this document as an embedded help book

Draw a line segment, rectangle, square, triangle, circle.

Select an "interesting point" (small square), e.g., vertex, midpoint, to popup information about an object and perform operations, which add "annotations".

Select/(tag)drag to (copy)move/reshape an object. Scrub to erase: annotations (2.x: if any), then object.

Shapes

LineSeg

A LineSeg displays its midpoint and two endpoints.

• endpoint: coordinates
• midpoint: coordinates, Length, Slope, Bisect Line command

Note: currently, y coordinates increase from top to bottom.

Rectangle

A Rectangle displays:

• corner: Perimeter
• top: Width
• side: Height
• center: Area

Square

A Square is basically a rectangle with equal sides, with several additional items:

• corner: Perimeter; Size
• center:
  • Area
  • Inscribe Circle: square's size is diameter
  • Circumscribe Circle: square's hypoteneuse is diameter

Circle

A Circle displays its center:

• coordinates; Area
• Inscribe, Circumscribe Triangle
• Inscribe, Circumscribe Square
• Inscribe, Circumscribe Hexagon

and a point on the circle:

• Radius; Circumference
• Tangent: line perpendicular to the diameter

Triangle

Vertex

A Triangle displays many points. For best results, try to make it large and/or non-symmetric. A vertex displays:

• coordinates
• angle°
• Bisect (Angle): line segment passes through "InCenter"
• Median: line segment from vertex to midpoint, passing through "Centroid"
• Altitude: line through vertex perpendicular to opposite side, passing through "OrthoCenter"

Side

A side displays its midpoint:

• coordinates
• Length
• Bisect Side: line perpendicular to side, passing through "CircumCenter"

Center

A triangle has several "centers":

• Orthocenter: intersection of altitudes (perpendiculars through vertices)
• Incenter: intersection of angle (vertex) bisectors; the center of an "Incircle", which fits inside the triangle
• Centroid: intersection of medians (lines between vertices and side midpoints)
• CircumCenter: intersection of side bisectors; the center of a "Circumcircle", which passes thru triangle vertices

Example

Draw a large, asymmetric triangle.

Select midpoint of each side and bisect; intersection is circumcenter; select circumcenter to draw a circumcircle. Scrub triangle once to erase annotations.

Bisect each angle, draw incircle.

Add Medians from each vertex; intersection is centroid.

Add Altitudes from each vertex; intersection is orthocenter.

GeoCnstr Versions

NewtonScript version of GeoCnstr is based on Smalltalk code for learning environments I wrote in the mid-'1970s .

GeoCnstr created with NewtDevEnv; it's 1.x/2.x compatible. Help book created from HTML by Newt's Cape. http://members.bellatlantic.net/~sweyer/newton/index.htm

Version 1.0 (11 Mar 1998)
Future: I may add other operations, objects (trapezoids, ellipses). Implement as stationery?

Distribute GeoCnstr

GeoCnstr is freeware, and may be distributed freely as long as all of the files are included and unmodified.

I may make GeoCnstr source available to registered NewtDevEnv users.

© Copyright 1997-98, S. Weyer. All Rights Reserved Worldwide.

Contact Author

Steve Weyer
17 Timber Knoll Drive
Washington Crossing, PA 18977-1052
Internet: weyer@kagi.com
America Online, Compuserve: SteveWeyer
http://members.bellatlantic.net/~sweyer/newton/index.htm