Two triangular billboards are installed on a highway. Let the billboards be represented by $△$ ABC and $△$ DEF. The billboards are mechanically designed in such a way that the names of the vertices of $△$ DEF are cyclically interchanged every 1 minute, i.e. the triangles remain the same way, only the names of the vertices change. At 10 AM, for the first time the positions of the billboards are such that we can say $△$ ABC≅ $△$ DEF. After x minutes, the billboards will be in such a way, that $△$ ABC≅ $△$ DEF for the second time. Find x.

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Solution

Since at 10 AM, we can write $△$ ABC $≅$ $△$ DEF, the congruency conditions for the next minutes would be:

$△$ ABC $≅$ $△$ EFD 10:01 AM

$△$ ABC $≅$ $△$ FDE 10:02 AM

$△$ ABC $≅$ $△$ DEF 10:03 AM

Therefore, after 3 minutes, we can say that $△$ ABC $≅$ $△$ DEF for the second time.

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Two triangular billboards are installed on a highway. Let the billboards be represented by $△$ ABC and $△$ DEF. The billboards are mechanically designed in such a way that the names of the vertices of $△$ DEF are cyclically interchanged every 1 minute, i.e. the triangles remain the same way, only the names of the vertices change. At 10 AM, for the first time the positions of the billboards are such that we can say $△$ ABC≅ $△$ DEF. After x minutes, the billboards will be in such a way, that $△$ ABC≅ $△$ DEF for the second time. Find x.

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Since at 10 AM, we can write △ABC ≅ △DEF, the congruency conditions for the next minutes would be: △ABC ≅ △EFD 10:01 AM △ABC ≅ △FDE 10:02 AM △ABC ≅ △DEF 10:03 AM Therefore, after 3 minutes, we can say that △ABC ≅ △DEF for the second time.