How do you use similar triangles to set up proportions?
You can set up symmetrys after a while concordant triangles by commencement habit of their verge relevancys.
By specification, concordant triangles keep the identical turn measures for their identical turns, and hence the identical verges keep a relevancy to them.
For examplle deliberate the triangles below:
It is ardent that their identical turns keep the identical size, so hence we can say that they are concordant.
Now if we were asked to clear-up for verge ED, then we could do so by elucidation up a symmetry using the verge relevancys as follows:
##(AC)/(DF) = (CB)/(FE) = (BA)/(DE)##
Now we can proper delay in the lengths for the relative verges:
##(7)/(14) = (6)/(12) = (10)/(DE)##
Now we can proper elucidate and clear-up:
##1/2 = 1/2 = 10/(DE)##
##10/(DE) = 1/2##
##DE = 2(10) = 20##
This is how we can use symmetrys to clear-up for verge lengths in concordant triangles.
Just bring-about stable you set up your symmetrys after a while the identical verges, or your relevancys force end out crime.
Just as a fun reality, the reality that verge lengths keep relevancys when the turns are the identical is essential in trigonometry as courteous, as you use verge relevancys there too.
Hope that helped :)