Descriptive Geometry/Mathematical Constructions/Addition/Subtraction

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.



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.



PRACTICE PROBLEM ]]

REFERENCES

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

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