Descriptive Geometry/Mathematical Constructions/Addition/Subtraction

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I) Addition : Finding the sum of parts using compass and straightedge:

Given length of two line segments AB and CD find the sum:
1) Starting with line m, construct a circle with radius equal to length of CD. Mark center of circle as point P, and where the circle intersects line m as point Q.
2) From point Q construct a circle with radius equal to segment AB. Mark the intersection of this circle and line m as point R.
3) The segment PR is equal to the sum of line segments AB and CD.


Addition Converted.jpg







The same principle for addition can be applied to subtracting segments.

II) Subtraction : Finding the difference of two segments using compass and straightedge:

Given length of two line segments AB and CD find the difference:
1) Starting with line m, construct a circle with radius equal to length of AB. Mark center of circle as point P, and where the circle intersects line m as point R.
2) From point R construct a circle with radius equal to segment CD. Mark the intersection of this circle and line m as point Q.
3) The segment PQ is equal to the difference of line segments AB and CD.


Subtraction Converted2.jpg






PRACTICE PROBLEM

AdditionProb01.jpg

Solution]]




















REFERENCES


http://www.vitutor.com/geometry/plane/line_segment.html

http://www.mathopenref.com/similartriangles.html