I don't follow, what do you mean by "We draw a parallel line to BC." and what is Y & Z?
If necessary I can do a drawing, anyone helping please ask if you wish me to draw a similar triangle for this explantion.
We start with an equilatral triangle and label the vertices top A, bottom left B and bottom right C.
We draw a parallel line to BC.
We have;
A to Y 2 units, Y to B 1 unit.
I should think that A to Z will also be 2 units and Z to C 1 unit.
I am asked to find the lengths of the parallels lines using ratios, however the following idea has too many unknowns I think and am wondering if another method is available?
(AY) / (YB) = (YZ) / (BC) = (2) / (1) = (x) / (x)
The problem here is that I can't solve the problem with more than one uknown?
Any ideas please
Trivial?
My last maths course teacher was a PHD.
One of my questions on that course was similar to this question here posted. The PHD gave a question about similar triangles and asked for the length of a side and the information given was a parallel side 5cm and an angle 65 degrees.
I worked out the other parrallel length which was 10cm, then I said tan 65 (10) = 21.4cm, which was the side length AB on that example.
The PHD said it was wrong and gave 0 out of 4 marks, then on the next example which was exactly the same the question asked for me to identify mistakes a student had made, I did and got 6 out of 6 marks, the PHD then wrote out the full solution and it was a mirror image of my last example?
How could that be wrong first and second time same thing its OK?
Solution;
We all can and do make mistakes, even with over 13000 posts.
Now before you get your back up, please remember that I am learning from first hand basics, and I am saying to you that I don't understand how you got BC = 3 when I am getting something different?
I am not saying you are wrong although it might seem that way, but as previously said I am somewhat confused because I don't understand?
I agree that I don't understand, however you are the experts!
I am advised that the length of BC = 3 from previous, however I have struggled with the basics as you all point out, but I ask again is the information given correct?
Similarity ratio;
(AY) / (AB) = (2) / (1) = 2/1
If I now use the product rule by BC = 3, then YZ = 6????
The parallel line YZ in the triangle above cannot ever be longer than the parrallel line BC?
Like I said I don't fully understand and you are the experts, but to me YZ = 3 and BC = 6
If you now believe that I am wrong, then please show the working out to justify your solution.
Thank you
David