# 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:

• 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.