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 Create 2 congruent triangles (Posted on 2017-10-31)
Given two segments in the same plane: AB and CD, of equal length.
Find point O such that the triangles AOB & COD are congruent.

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 solution | Comment 2 of 4 |
Connect each endpoint of AB to opposite endpoints of CD. As there are two ways of doing this, the general case will be that each way (A to C and B to D vs A to D and B to C) will produce different congruent pairs. Sometimes one of the ways will not produce one.

Construct the perpendicular bisector of the two previously constructed segments. Point O will be where the two perpendicular bisectors meet.

Note
1.The lines shown ae DE and BC. I thought I had labeled them correctly but they got mislabeled.
2. the circle centered on C was placed in order to construct BC as being the same length as DE.

Edited on October 31, 2017, 10:33 am
 Posted by Charlie on 2017-10-31 10:23:52

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