Proof- triangles

1. Sep 30, 2004

Blissfulpain

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 : )

next...

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 :)

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• Triangle Diagram.png
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2. Sep 30, 2004

nolachrymose

Hint: angle bisector theorem.

Hope that helps!

3. Sep 30, 2004

Blissfulpain

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

4. Oct 1, 2004

Gokul43201

Staff Emeritus
No right angles required, merely an understanding of the words adjacent and opposite.

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.

5. Oct 1, 2004

Blissfulpain

so, 3/x=4/7
3/x=1.75
x=1.75*3
x=5.25
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 )))

6. Oct 5, 2004

Blissfulpain

oops... i mean 3/7=x/4
so 3/7=.429
.429x4=1.7 units

therefore BD=1.7