Fundamental Elements of Practical Geometry
In this page, a short and to-the-point summary of the four elements of practical geometry is provided.
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In practical geometry, we study about constructing
• line segments,
that make different plane-figures like triangles, rectangles, quadrilaterals, etc. Which of the following is a fundamental to practical geometry?
- constructing a line, an arc, an angle, and a parallel
- constructing collinear points, equidistant points, equiangular points, and parallel line.
- both the above
- both the above
The answer is "both the above"
The fundamental elements of practical geometry are
1. constructing a straight line using a ruler (which are points collinear to two points).
2. measuring a distance using a compass and marking an arc (which are points equidistant to the center).
3. measuring an angle using a protractor and marking a ray with the angle (which are points equiangular to the initial point)
4. constructing a parallel using set squares (which are points on a line parallel to a given line)
In the course of the lessons, the secondary elements and the end-applications will be explained. For example, bisecting a line or constructing a parallel line using a compass are some examples of secondary elements. The primary elements are used to construct the secondary elements.
And, constructing a square using the length of a diagonal or constructing a parallelogram are some examples of end-applications. These constructions use combination of primary and secondary elements.
Fundamental Elements of Practical Geometry :
1. constructing a line connecting `2` points
2. constructing an arc of given radius
3. constructing an angle of given measure
4. constructing a parallel at a given distance to a line