|Sep30-04, 08:57 PM||#1|
ok, i'm in first year coolege and we're doing some review from highschool work.. but i can't for the life of me remember how to do one of these questions and i can't seem to get past this one part or at least figure out how to prove that it is what i think it is.
it's gonna be a bit trickier, cuz i can't insert a picture, but i guess that isn't of the most importance anyways. alright
you have triangle ABC.
side AB=4 units
side AC=7 units
the line CD extends for 3 units towards point B, the distance between point B an D is unknown and is what needs to be found
the Angle BCD is = angle DAC
here's what i've tried to do so far...
i've tried to fold the 2 triangles in half across the line AD, which lines up the two sides AB and AC, with the line AC extending 3 units futher then line AB. I'm still trying to follow this train of reasoning.. but so far with little success, i don't really know what to do next, but i think it helps somehow : )
I tried extending the common side between the two triangles, line AD, far enough so that i can draw a new line, 7 units long, from point C, i'll call the intersection point E. The problem arises when i can't prove that the new triangle DEC is the same as triangle ADC. I CAN prove that it is proportional to triangle ABD, but that doesn't help me, because i only know that the side CE is 7 units, the Side DC is 3 units, and i don't know if i can prove that the angle DEC is equal to the angle DAC... which means i can't prove that the line DE is a continuation of the line AD...
hence i'm lost.
thx for the help in advance.. hey, kewl... just found the attacthment thing... i'll go draw a picture and then post :)
|Sep30-04, 09:14 PM||#2|
Hint: angle bisector theorem.
Hope that helps!
|Sep30-04, 11:10 PM||#3|
nope, doesn't help... i looked it up on the net, and got this "The angle bisector of an angle in a triangle divides the opposite side in the same ratio as the sides adjacent to the angle."
so the angle bisector is line AD, and the adjacent and opposiye side are? i can't assume ANY right angles... and all the other stuff i found on this theorem had something to do with area of a triangle, which i can't do either, because i don't have enough info to find that yet...
a bit more of a hint is needed
|Oct1-04, 01:02 PM||#4|
Let me paraphrase the theorem for the triangle you've got :
Simply, it says that CD/BD = AC/AB.
Now go back and understand what the theorem is trying to say.
|Oct1-04, 03:09 PM||#5|
huh, i had gotten that number before... just couldn't prove that it was the right number... now i can with that theorem
thx a lot guys :)))))
|Oct5-04, 01:04 PM||#6|
oops... i mean 3/7=x/4
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