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Mathematics
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Jun 1st, 2015

they are congruent if they are of equal size and shape,

to describe them we calculate their lengths

A(-5,1),B(-4,3),C(-1,1) and A`(9,-3), B`(8,-1), C`(5,-3)

so AB=sqrt{(-5+4)^2+(1-3)^2}=sqrt5 and A`B`=sqrt{(9-8)^2+(-3+1)^2}=sqrt5

implying AB=A`B`

also BC=B`C`=sqrt{3^2+2^2}=sqrt13

also AC=A`C`=sqrt{(-5+1)^2+(1-1)} or sqrt{(9-5)^2+(-3+3)^2}=4

hence in summary AB=A`B`, AC=A`C` and BC=B`C`

and AB//A`C` , BC//B`C`, AC//A`C`

so triangle ABC~A`B`C`


Jun 1st, 2015

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