Similar Triangles

LCHL

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May 21, 2015
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Hi all. Sorry for the poor quality photo. I wouldn't include it if the diagram wasn't necessary.

DSC_0064.jpg

The answers at the back of the book are (ii), 80/3 and (iii), 128/3.

I could get part (i) without issue, but I have issues onwards.

DC=16, so AB=16 (Parallelogram)
Based on the information given, AB is 0.6x the size of CE, indicating to me that CE=80/3.

80/3 + 16 = 128/3, which is not the answer that the book is giving me.

I have no idea how to get AD. If I could get BF or FC, I could scale it up appropriately or use the similar triangle ratio forumula, but I don't know how to get them either.

To get an idea of the level that I'm at, I'm 18 and doing Irish Leaving Certificate Maths at Higher Level, which is the hardest difficulty exam of the final secondary education/high school test I have to do in Maths. This question is in my textbook, and to be perfectly honest, I wouldn't be surprised if there's an error, given that we've found multiple errors over the years. There is a list of 22 theorems that we are required to know, which can be found in the curriculum. https://www.google.ie/webhp?sourcei...pv=2&ie=UTF-8#q=leaving cert maths curriculum

Thank you.:)
 
Hi all. Sorry for the poor quality photo. I wouldn't include it if the diagram wasn't necessary.

View attachment 5331

The answers at the back of the book are (ii), 80/3 and (iii), 128/3.

I could get part (i) without issue, but I have issues onwards.

DC=16, so AB=16 (Parallelogram)
Based on the information given, AB is 0.6x the size of CE, indicating to me that CE=80/3.

80/3 + 16 = 128/3, which is not the answer that the book is giving me.

I have no idea how to get AD. If I could get BF or FC, I could scale it up appropriately or use the similar triangle ratio forumula, but I don't know how to get them either.

To get an idea of the level that I'm at, I'm 18 and doing Irish Leaving Certificate Maths at Higher Level, which is the hardest difficulty exam of the final secondary education/high school test I have to do in Maths. This question is in my textbook, and to be perfectly honest, I wouldn't be surprised if there's an error, given that we've found multiple errors over the years. There is a list of 22 theorems that we are required to know, which can be found in the curriculum. https://www.google.ie/webhp?sourcei...pv=2&ie=UTF-8#q=leaving cert maths curriculum

Thank you.:)

I have not worked on yet - but you did take into account of the fact that:

\(\displaystyle \Delta ABE\) ≡ \(\displaystyle \Delta ECF\) ≡ \(\displaystyle \Delta EDA\)
 
How is ABE congruent to ECF? I see how ECF is similar to EDA.
 
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