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Sum of given segments

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See also the animated version.

After doing this Your work should look like this

Start with three given segments a, b and c

1.  Mark a point P towards the left of the work area.
2.  Draw a long line from P to the right.
3.  Set the compasses width to the length of the segment a.

(Note: We can use the given segments in any order.)
4.  Without changing the compass width, place the point on P and make an arc across the line.
5.  Set the compasses width to the length of the segment b.
6.  Without changing the compass width, place the point on the previous arc and make an arc across the line to its right.
7.  Set the compasses width to the length of the segment c.
7.  Without changing the compass width, place the point on the previous arc and make an arc across the line to its right, creating point Q.
Done. The segment PQ has a length which is the sum of the segments a,b and c.
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Non-Euclidean constructions