Trapezoid: ABCD is a trapezoid whose diagonals AC and BD intersect at point E.

AWildZeebra

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ABCD is a trapezoid whose diagonals AC and BD intersect at the point E. If AB = 2/3 DC, prove that AE = 3/5 AB + 2/5 AD.
My teacher recommended using triangles to solve, I tried something else but I'm not necessarily sure if it works and I don't know how to approach it with triangles.
So if you don't mind letting me know if my current answer is correct or not, but also potentially giving me a hint in solving it with triangles.
Thank you
 

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ABCD is a trapezoid whose diagonals AC and BD intersect at the point E. If AB = 2/3 DC, prove that AE = 3/5 AB + 2/5 AD.
My teacher recommended using triangles to solve, I tried something else but I'm not necessarily sure if it works and I don't know how to approach it with triangles.
So if you don't mind letting me know if my current answer is correct or not, but also potentially giving me a hint in solving it with triangles.
Thank you

I can't follow your reasoning; it looks like you are starting with what you were told to prove.

I'm also not sure what you were told to prove, as you stated it here in terms of what appear to be lengths (and you don't mention vectors in the problem statement at all), but in your work you turn it into a vector sum. Please make the problem clearer. (I'll use bold for vectors.)

One step in your work is definitely wrong. You go from 6/15 DC + 6/15 AD to 12/15 AC, when it should be 6/15(DC + AD) = 6/15 AC. (You also could have simplified fractions and saved work, but that isn't an error in itself.)
 
ABCD is a trapezoid whose diagonals AC and BD intersect at the point E. If AB = 2/3 DC, prove that AE = 3/5 AB + 2/5 AD.
My teacher recommended using triangles to solve, I tried something else but I'm not necessarily sure if it works and I don't know how to approach it with triangles.
So if you don't mind letting me know if my current answer is correct or not, but also potentially giving me a hint in solving it with triangles.
Thank you
You want to prove/show that AE = 3/5 AB + 2/5 AD so you can't assume that it is true. Otherwise every think is true?

EX: Claim is that 2=3. Proof: 7=7, 2*7 = 2*7 and 2=3. Done
 
Alright I'm starting with the AB = 2/3 DC and working from there but no matter what I seem to do I can never get a denominator of 5 and I seem to be just going around in circles with the variables. Is there another approach besides looking at it for example like AB = AE + EB or AB = AD + DC + CB and doing stuff like that. Or I could be just doing this wrong not sure
 
Alright I'm starting with the AB = 2/3 DC and working from there but no matter what I seem to do I can never get a denominator of 5 and I seem to be just going around in circles with the variables. Is there another approach besides looking at it for example like AB = AE + EB or AB = AD + DC + CB and doing stuff like that. Or I could be just doing this wrong not sure

Please at least state the problem clearly. Can you confirm that the problem is to prove a vector equation, not just a statement about lengths as you appeared to be saying?

One place to start is with similar triangles. Can you see such a pair, and use it to find the ratio of lengths of AE to EC, for example?

Once you find the ratio of AE to AC, you can write AC as AD + DC and do a little algebra. The main idea is to start with what you want (AE) and express it in terms of things that can be expressed in terms of AB and AD.

Don't be looking at the coefficients; they should come out by themselves. Focus on the vectors you want to use.
 
but no matter what I seem to do I can never get a denominator of 5
Whatever equation you have, simply divide by 5. This is a technique I use all the time to get something to look closer to what I want.
 
Ive been working on it for the past couple days and cant seem to come up with anything. Ive tried looking into similar triangles but I dont understand how that applies here, if someone doesn't mind potentially giving me a step in the right direction to whatever answer they get Id really appreciate it! But as of right now Im pretty lost and its due tomorrow. Im also not exactly sure why my previous answer doesnt work besides the fact that there is the mathematical error that Dr. Peterson pointed out. Any help would be much appreciated. Thanks
 
This is what my current best answer is

Your picture is almost impossible to read. Please try again; one way to get an image that will upload well is to use the Windows "snipping" tool to copy an image that is readable on your screen. Or you can use suggestions here for uploading bigger images.

But from what I can read, you still seem to be starting with what you are supposed to prove. You can't do that.

Have you tried my suggestion?

One place to start is with similar triangles. Can you see such a pair, and use it to find the ratio of lengths of AE to EC, for example?

Once you find the ratio of AE to AC, you can write AC as AD + DC and do a little algebra. The main idea is to start with what you want (AE) and express it in terms of things that can be expressed in terms of AB and AD.

Do you see any similar triangles? Can you in any other way write AE as a number times AC? That is my starting point.
 
Wow I got it, thank you so much for the help! I went back and looked and what you said earlier and it all came together
 
I found that ratio through assuming it was right though so I think I need to find it another way
 
Suggestion: label your lines; like a = AB, b = BC ...
Much less writing, plus clearer equations...
 
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