Question 1064443: Hay!! I need help with my pre-algebra homework, I have tried everything and your my last hope, again, if you can help thank you SO much. :)
Problem: Given Triangle ABC ~ Triangle DEF, tell whether the given information is enough to find the specified measurements. Explain your thinking.
a.) You know AB, BC, CA and DE. You want to find EF and FD
b.) You know AB, BC and FD. You want to find CA.
a and b are both separate problems, again, thank you SO much!!!! :)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the triangles are similar, then their corresponding sides are proportional.
this means that:
BA / DE = BC / EF = CA / FD
part a.
you know the measurements of AB, BC, and CA from the first triangle.
you know the measurement of DE from the second triangle.
you want to find the measurements of EF and FD from the second triangle.
use what you know to find what you don't know.
DE from the second triangle corresponds to AB from the first triangle.
EF from the second triangle corresponds to BC from the first triangle.
FD from the second triangle corresponds to CB from the first triangle.
since you know the measure of DE from the second triangle and you know the measure of AB from the first trangle, your common ratio is known.
since you alwo know BC and CA from the first triangle, you can use that ratio to find the measure of EF and FD.
you get:
DE / AB = EF / BC = FD / CA
DE / AB gets you the common ratio.
that common ratio allows you to solve for EF / BC and FD / CA.
for example:
assume AB = 3 and BC = 5 and CA = 4
assume DE = 6.
your common ratio is DE / AB = 6/3 = 2
to find EF, you set that commmon ratio equal to EF / BC.
you get 2 = EF / BC.
since BC = 5, you get 2 = EF / 5.
solve for EF to get EF = 10
similarly, you will get FD = 8.
triangle ABC sides are 3,5,4 respectively.
triangle DEF sides are 6,10,8 respectively.
the triangle as similar because all their corresponding sides are proportional.
part b.
same triangles.
you know the measure of AB and BC from the first triangle.
you know the measure of FD from the second triangle.
you know that, since the triangles are similar, that:
AB / DE = BC / EF = CA / FD.
you want to find the measure of CA.
you know the measure of AB and you don't know the measure of DE, so you can't find a common ratio there.
you know the measure of BC and you don't know the measure of EF, so you can't find a common ratio there.
you don't know the measure of CA and you know the measure of FD, so you can't find the common ratio there.
you will not be able to find the measure of CA from the information given.
you need a minimum of the measure of one side of the first triangle and the measure of the corresponding side of the second triangle in order to find the common ratio.
once you know the common ratio, you need a minimum of the measure of one side of either the first triangle or the corresponding side of the second triangle to find the measure of the unknown side of the corresponding pair.
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