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[Label1]
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[Label2]
Caption=Let's now put another vertex~~at any place on the second line.~~We can now reconstruct an equilateral triangle,~~because we know two of its vertices.
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[Label3]
Caption=An equilateral triangle has all its sides equal.~~We know one of the sides (AB). The third vertex~~is equally distant from both A and B, so let's just~~describe two circles with radius AB around points~~A and B. They'll intersect at two points which will~~be at distance AB from both points A,B.~~~~Let's finally pick one of these two intersection points~~(any one) and draw the triangle.
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[Label4]
Caption=But there is a problem: we have chosen point B arbitrarily,~~and the third vertex C doesn't lie on the third line! What shall we do?~~~~There's nothing too scary. Let's investigate, maybe our triangle is not that bad?~~Move point B until vertex C lies on the third line.
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Message=Just because you can't move point B for C to lie PRECISELY on the line. You have to specify AN ALGORITHM of construction of point C, and your freehand adjustings cannot be a part of an algorithm.

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Path=3LinesTriangle4.dgf

