Descriptive Geometry/Mathematical Constructions/Multiplication/Division

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I) Multiplication : Finding the product of segments
Given line segments l and m:
1) Construct line l.
2) Construct line m using the same origin point as line l, using an arbitrary angle.
3) Draw a line equal to 1 on line m and connect the endpoint of that line to the line l, creating a triangle.
4) Construct a line at the end of line m parallel to the previous construction line made in step 3, extend the line l if needed.
5) The segment lm is the product of lines l and m.


Multi Converted.jpg







II) Division : Diving a segment into equal or unequal parts

Unequal segments:
Given length of line lm; divide into two unequal lengths
1) Construct line lm.
2) Construct an arbitrary line using endpoint of line lm.
3) On this line, mark out desired lengths.
4) Connect the last desired point of division to m.
5) Using the line created in step 5, construct similar parallel lines to each division point, dividing up the given line into as many segments as desired.


Div Converted.jpg






We can also divide a segment into an equal number of segments:


Equaldivision Converted.jpg






PRACTICE PROBLEM


DivProb02.jpg

Solution]]



















REFERENCES

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

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