Thread: Finding similar triangles using ratios

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

I don't follow, what do you mean by "We draw a parallel line to BC." and what is Y & Z?

Originally Posted by pickslides

I don't follow, what do you mean by "We draw a parallel line to BC." and what is Y & Z?

I'll upload a diagram with the details on it.
Hope this makes it easier to understand

Thanks
David

Originally Posted by David Green

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.

Correct

Originally Posted by Plato

Correct

But I have not found the ratios of YZ and BC?

This is the part I am struggling with?

Originally Posted by David Green

But I have not found the ratios of YZ and BC?

This is an equilateral triangle so .
Carry on.

Originally Posted by Plato

This is an equilateral triangle so .
Carry on.

I worked it out at YZ = 1.5

Originally Posted by David Green

I worked it out at YZ = 1.5

I don't know what that means.

Originally Posted by Plato

I don't know what that means.

Sorry I think I got the fraction wrong way round?

2 / 3 x 3 = 2

The ratio 3:2 I think but there are suppose to be two answers also?

Originally Posted by David Green

I worked it out at YZ = 1.5

look at your diagram and describe triangleAYZ

If the parallel BC = 3, and the triangle is equilateral, then each vertex should be 60 degrees, if this is so then;

tan 60 x 3 = AB = 5.2?

However the given information advises AB = 3

So I am confused?

Originally Posted by David Green

Sorry I think I got the fraction wrong way round?

@Mr. Green
You are the one who struggles with even the most basic mathematical concepts. Therefore, if I were you I would pause and wounder why someone with over 13000 posts might be wrong about something so trivial.

Originally Posted by Plato

@Mr. Green
You are the one who struggles with even the most basic mathematical concepts. Therefore, if I were you I would pause and wounder why someone with over 13000 posts might be wrong about something so trivial.

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?

Originally Posted by David Green

I worked it out at YZ = 1.5

If it isn't OBVIOUS to you that YZ = 2, (and are trying to make it equal to 1.5)!,
then I agree with Plato: you need to get back to basics.

Originally Posted by Wilmer

If it isn't OBVIOUS to you that YZ = 2, (and are trying to make it equal to 1.5)!,
then I agree with Plato: you need to get back to basics.

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