Geometry: Similar Shapes

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The discussion centers on the calculation of two possible values for x in similar triangles, where the relationships between the sides are explored through scale factors. Participants highlight the importance of understanding the assumptions regarding side relationships, particularly between segments CD and BE, which may not be parallel despite appearing so. The conversation emphasizes that similar triangles maintain proportional relationships in their corresponding sides and angles, but the diagram's misleading scale complicates the problem. The need for careful analysis of the diagram is stressed, as it can lead to misconceptions about the properties of the triangles involved. Ultimately, the challenge lies in recognizing the trickiness of the problem and the necessity of rigorous geometric reasoning.
  • #101
TensorCalculus said:
Do you want me to tell you or would you rather work it out yourself?
You've assumed that ##AB:AE=AC:AD## - in the other case that isn't true
Can you give me a little nudge, just a slight hint?
 
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  • #102
Similar triangles means that they have all the same angles. What's the other option for the triangles to be similar in this case, if that assumption isn't true?

Edit: if you want a little more help, what if ##AE:AC = AB:AD## ?
 
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  • #103
Beyond3D said:
Can you give me a little nudge, just a slight hint?
It's already posted! See diagram in Post #91.
 
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  • #104
Steve4Physics said:
It's already posted! See diagram in Post #91.
Oh wow, I just realised, we let this thread drag on 104 messages... feels like it was only 10 messages long like 2 seconds ago :cry:.
 
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  • #105
Let me add to the clutter to re-emphasize:
If you make an assumption and it leads to a valid solution, that does not invalidate the solution!! It does not, however, validate the assumption.
I am beginning to love this question. Often I get to a solution by making a guess. One cannot be blinded into assuming this guess becomes truth. Therein lies the path to ruin. In this question, the presence of an "official" drawing is problematic. Perhaps the question should first ask for two drawings ? I don't really see a cleaner way to present this in a text.
 
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  • #106
What I really want to do now is find out who the writer of this exam question was and email them a link to this thread: just for fun!! Wonder what the reaction would be.
 
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  • #107
TensorCalculus said:
What I really want to do now is find out who the writer of this exam question was and email them a link to this thread: just for fun!! Wonder what the reaction would be.
Well done - you extended the thread to 4 'pages'! So I won't feel guilty about adding this...

Beyond3D said:
$$\ AB:AE=AC:AD$$
$$\frac{8cm}{12cm}=\frac{x+8cm}{15cm}$$
$$15\cdot\frac{8cm}{12cm}=15\cdot\frac{x+8cm}{15cm}$$
$$\frac{120}{12}=x+8$$
$$\ 10 = x+8$$
$$\ x=2$$
FWIW, there's quicker method. One of the solutions requires BE to be parallel to CD (which is evident when you do a drawing). So you can use the intercept theorem and immediately write (with all values in cm):
##\frac x8 = \frac 3{12}## so ##x = 8 \times \frac 3{12} = 2##.
(But this is not applicable to the other solution.)
 
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  • #108
TensorCalculus said:
Oh wow, I just realised, we let this thread drag on 104 messages... feels like it was only 10 messages long like 2 seconds ago :cry:.
There is nothing that extends a thread more than two different opinions! I remember a seemingly endless thread about the existential question whether ##0## is real. Or start a thread by asking whether ##\dfrac{1}{2}=\dfrac{2}{4}## represents an equivalence relation or actual equality. It will be hilarious. And bloody.
 
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  • #109
fresh_42 said:
There is nothing that extends a thread more than two different opinions! I remember a seemingly endless thread about the existential question whether ##0## is real. Or start a thread by asking whether ##\dfrac{1}{2}=\dfrac{2}{4}## represents an equivalence relation or actual equality. It will be hilarious. And bloody.
okay time to start a thread about 1/2 = 2/4
 
  • #110
TensorCalculus said:
What I really want to do now is find out who the writer of this exam question was and email them a link to this thread: just for fun!! Wonder what the reaction would be.
Maths Genie
https://www.mathsgenie.co.uk/resources/1hnov2017B.pdf
Q.22
 
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  • #112
TensorCalculus said:
I'll have to hunt down the people who wrote the Edexcel gsce maths papers no?
Ah, I see what you mean. Yeah.
 
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  • #113
paulb203 said:
Homework Statement: See screenshot in main body
Relevant Equations: I don't know if there is a generic equation
Maybe something like AB(SF)=AC ?

View attachment 363169
Why are there two possible values of x?

Here's what I've done so far.

AE(SF)=AD
12(SF)=15
SF=15/12
=5/4

AB(SF)=AC
8(5/4)=AC
AC=10

AC-AB=x
x=10-8
x=2

A hint please, as to my next step
A jocular note:
I didn't know that "similar" was a mathematical term.
Proportional would have appropriate.
Unless the intended effect was to turn Thales on his grave with this much ado about nothing.
 
  • #114
Thanks to @pbuk I knew the origin of the question (edexcel GCSE maths papers) but sadly they don't reveal the names/contacts of the individual question writers... what does everyone think about emailing this address? General Edexcel contact:
examsofficers@pearson.com
I am very curious as to how they will react to our very... thorough analysis of their question :D
 
  • #115
Patxitxi said:
A jocular note:
I didn't know that "similar" was a mathematical term.
Proportional would have appropriate.
Unless the intended effect was to turn Thales on his grave with this much ado about nothing.
Proportional only refers to two quantities; similarity refers to all quantities, here three side lengths or three angles. It is a stronger condition that proportional would be.
 
  • #116
TensorCalculus said:
but sadly they don't reveal the names/contacts of the individual question writers
Probably for the best. I can only imagine them being signed up for tons of spam emails by chuffed students if their emails were public.
 
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  • #117
Muu9 said:
Probably for the best. I can only imagine them being signed up for tons of spam emails by chuffed students if their emails were public.
oh that makes sense.
I'm going to mail their main contact email anyway - just for fun! Maybe they will find it interesting to see such an opinionated converstaion about their question. They probably never expected people would think so hard about it haha.

Or maybe they will do what most do and ignore me. In that scenario, at least it was worth a try
 
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