ELEMENTARY AND BASIC CONSTRUCTIONS IN GEOMETRY
ELEMENTARY AND BASIC CONSTRUCTIONS IN GEOMETRY
1. Elementary Constructions
In geometry, the allowed drawing tools are ruler (with no marking on it, also known as straightedge) and a compass.
Elementary constructions are the constructions of:
an arbitrary point;
an arbitrary line;
an arbitrary line through a given point;
a line (segment, ray) through two given points;
an arbitrary circle;
a circle with center in a given point and a radius equal to the length of a given segment;
an arbitrary point on a given figure;
the intersection point of two lines, of a line and a circle, of two circles (if existing).
Use the buttons of GeoGebra and create the elementary constructions.
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Problem 1. Construct a segment equal to a given segment.
Construct the segment on the ray CD. Use the button compass, to "move" the segment.
Describe the construction in your notebook. |
Follow the construction step by step, by using Navigation bar for construction steps and Construction protocol. |
The construction with Geogebra is done as follows:
1. Given are a segment and a ray - we construct those with the segment button AB and the ray button CD.
2. Similar to the paper-and-pencil drawing, we use the button compass to construct a circle: open the compass by using the given segment AB and construct a circle d with center point C and radius equal to the length of the segment AB.
3. We create the intersection point Е of the circle and the ray.
4. The segment CE is the one we sought.