Math Is Fun Forum

harrychess

Member

Registered: 2014-04-04

Posts: 33

Similar TRiangles

In triangle ABC, points X and Z are on AB and Y is on AC such that XY is parallel to BC and Zy is parallel to XC. If AZ = 8 and ZX = 4, then what is XB?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Similar TRiangles

hi harrychess

Those parallel lines make some similar triangles.

First show that AZY and AXC are similar.

From that you can get the ratio AY:YC

Now show that AXY and ABC are similar.

From that you can get AX:XB

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Similar TRiangles

Hello harrychess:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Similar TRiangles

Last edited by ElainaVW (2014-06-23 06:39:14)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Similar TRiangles

You've done such things yourself, bobbym.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

Of course I have done some EM before.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Similar TRiangles

That was in response to post #4.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

So, then we are agreed, I have done some EM before.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Similar TRiangles

You have done EM, but you also blurted out answers before.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

Yes, but I have a certain madness in my blurtations. A certain set of rules.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Similar TRiangles

Those are not the forum rules, but rather your own. What prevents EVW from developing her own set of rules for blurting answers out?

Last edited by anonimnystefy (2014-06-23 12:54:09)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

Those are not the forum rules, but rather your own. What prevents EVW from developing her own set of rules for blurting answers out?

My rules are not arbitrary.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Similar TRiangles

They still apply to you only.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

Well, that makes sense. My rules should apply to me.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Similar TRiangles

So, your comment in post #4 is not a good one, then?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

I am not following you?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Similar TRiangles

You told her to check the forum rules before blurting out, but there are, in fact, no forum rules on blurting out.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Similar TRiangles

There are no forum rules for blurting out.  However, as post #4 says for EVW alone, the rest of us will not know what it says.

When someone asks for help, I try to do just that.  I give hints, suggest ways of tackling the problem, etc.  I try to avoid giving the answer, since I think it's best for the poster to find that for themselves.  Result of 37+ years of being a teacher I suppose.  I'm surprised that you would use experimental maths to solve this question.  Does that mean you drew, say, 100 triangles, each with the given lengths, then measured XB in each, before calculating the mean and standard deviation to assess the reliability of your answer.  Of course, that only shows that the answer lies close to your chosen value.  I suppose you could state a confidence interval.

Myself, I prefer to use Euclidean geometry; a straight forward calculation in my head; leading to a value that is good for all triangles with the given properties.  Of course, I haven't tested whether my result still holds on the surface of a torus, but I took it as implicit from the wording of the question and the post title, that Euclidean rules apply here. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

You told her to check the forum rules before blurting out, but there are, in fact, no forum rules on blurting out.

There are no forum rules for blurting out.

Perhaps no hard fast rule but if an earlier poster does not supply the answer, (post #2). It means that he is requesting that the OP think about it on his own. If someone overposts with the answer then the whole point of the earlier post is lost. Indeed it is an unnecessary temptation to peek.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Similar TRiangles

I try to avoid giving the answer, since I think it's best for the poster to find that for themselves.

I am truly sorrow and will follow that suggestion. I can see how Bob might have wanted him to use his own head.

My rules are not arbitrary.

I can live by them.

I'm surprised that you would use experimental maths to solve this question.  Does that mean you drew, say, 100 triangles, each with the given lengths, then measured XB in each, before calculating the mean and standard deviation to assess the reliability of your answer.  Of course, that only shows that the answer lies close to your chosen value.  I suppose you could state a confidence interval.

Hello Bob, no I didn't use that method but I would prefer that to having no answer. If necessary a simulation is always an option, I would do millions of them not a hundred. This would get about 3 digits of precision and a bound which might be good enough.

Why use experimental math? The best answer might be because it works. The first rule taught to me by my two teachers was to transform each problem into what I was good at doing. One called it the "home court advantage," the other said it was Sun Tzu's favorite motif to fight every battle on terrain that was favorable. Instead of thinking about the problem in terms of the language that is obvious ( in this case Geometry ) each problem is changed over into the same paradigm.

The old way of solving problems demanded that we be experts in Geometry, Calculus, Linear Algebra, Group theory, Abstract Algebra, etcetera. That meant if you don't know each discipline as well as the person who wrote the problem you couldn't do the problem. Conversion to experimental math means knowing only one field as well as an expert.

The proof of the pudding is in the eating. Did I get the right answer?

I also got the answer faster than bobbym.

Last edited by ElainaVW (2014-06-23 20:22:21)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Similar TRiangles

I also got the answer faster than bobbym.

Yes you did! But take care to notice that when I was your age I was the fastest on the planet. Not this planet, a much smaller one...

You did not answer my question.

About the pudding, please do not quote pappym. He is long gone and some of us believe they can not rest when they are being quoted constantly.

I am glad you are reading Sun, you will learn much from him.

About the EM, you are only making the first and most basic observation. You left out a whole boatload of truth.

Pragmatism is a philosophical movement that includes those who claim that an ideology or proposition is true if it works satisfactorily.

Doing what works is the first rule of EM.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Similar TRiangles

Did I get the right answer?

Well you got the same as me.  Is that good enough ? 

Often posters for help don't just want to know the answer; they may be doing a course where their teacher expects them to write down a method.  Indeed, in the UK sometimes the answer only carries a single mark and there may be several more for how you got it.  Whether you can assume that an answer alone will get you all the marks depends on the course.  So I usually assume that is what a poster needs and explain the 'how' , if I can.  Two other advantages:  (1) the poster has to do some thinking (which I always think is a good thing)  and (2) they might, as a result, be able to do the next one on  their own.

If I can see how to do a question, then that's enough.  If I cannot then I do a trial or two.  This post

http://www.mathisfunforum.com/viewtopic.php?id=21105

is a good example.  Once I had some data I could see a way to get a watertight answer by algebra.  By watertight I mean I was able to show that I had all the values and also that these were exact values not just close approximations.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: Similar TRiangles

please do not quote pappym. He is long gone and some of us believe they can not rest when they are being quoted constantly.

Poor Einstein and all those famous people.

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.