I always have trouble with this type of problem...

[XxHelpMePlzxX]

I always get stuck on these problems, and was wondering if anyone could explain it to me.

 

[Deleted member 4993]

I always get stuck on these problems, and was wondering if anyone could explain it to me.

View attachment 33313

What does AB ~ AD mean?

Where is point E of triangle AEF?
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[XxHelpMePlzxX]

View attachment 33314

What does AB ~ AD mean?

Where is point E of triangle AEF?
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

First of all if you are trying to help someone with geometry you should know what AB≅AD means, secondly point E is where line FC intersects with line AD (sorry for not making that clear beforehand). As for where I'm stuck, its the entire process that I don't get, hence why I didn't explain where exactly I got stuck.

 

[Dr.Peterson]

I always get stuck on these problems, and was wondering if anyone could explain it to me.

View attachment 33313

I can explain how to start.

First, observe that the diagram is (intentionally) inaccurate; AB and AD don't look like the same length, and (assuming E is the only unlabelled intersection point in the diagram) triangle AEF doesn't look isosceles. You can't even tell which two sides are supposed to be equal.

So a good first step is to draw a more accurate picture, which will help you guess what the goal is, and see some implications of the "givens". (I've done that for myself, but since doing it is part of the work, from which you are supposed to learn something, I'm not showing it to you.)

While you're drawing it, label the equal segments and the right angle, and then start labeling other things that are equal, notably angles. (Sometimes it's good to do that with variables.) Do that enough, and you may see the proof sitting in front of you. Then your only remaining task will be to write it out.

Let's see what you can do. That's the only way to learn how not to get stuck.

 

[blamocur]

First of all if you are trying to help someone with geometry you should know what AB≅AD means

I feel like an impostor since I've been helping people with geometry for quite some time but still don't know what [imath]\cong[/imath] means here. In LaTeX the corresponding command is called \cong, which might stand for 'congruent', but I thought this term is used for triangles, not for line segments.
Can someone please enlighten me about the exact meaning of this symbol in geometry?
Thank you.

 

[Dr.Peterson]

I feel like an impostor since I've been helping people with geometry for quite some time but still don't know what [imath]\cong[/imath] means here. In LaTeX the corresponding command is called \cong, which might stand for 'congruent', but I thought this term is used for triangles, not for line segments.
Can someone please enlighten me about the exact meaning of this symbol in geometry?
Thank you.

Congruence applies to any figures that are exactly the same size and shape, including line segments:

Congruent Lines Definition - Math Open Reference

www.mathopenref.com

In this case, it's equivalent to [imath]|AB|=|AD|[/imath].

 

[Dr.Peterson]

First of all if you are trying to help someone with geometry you should know what AB≅AD means.

Often in helping students, we ask questions not in order to learn something, but to get the student to think about what they know, and tell us. Have you never had a teacher who asked such questions of you?

As for where I'm stuck, its the entire process that I don't get, hence why I didn't explain where exactly I got stuck.

In this case, the fact that you know the definition means that you are not unable to do anything at all! You are stuck at some point after interpreting what the problem is asking. We want to see what you have tried, even if you think it is nothing, because there will often be something in there that we can use.

And if you haven't tried at all, that's a problem. You don't learn without trying.

 

[pka]

I always get stuck on these problems, and was wondering if anyone could explain it to me.

View attachment 33313

We assume that [imath]\{E\}=\overline{AD}\cap\overline{FC}[/imath]
Note that the vertical angles at [imath]E[/imath] are congruent. So [imath]\angle AEF\cong \angle CED[/imath].
Can you argue that [imath]m(\angle B)+m(\angle F)=m(\angle CED)+m(\angle D)[/imath]? [think complementary angles]
If you do so then you can finish!


[imath][/imath][imath][/imath][imath][/imath][imath][/imath]

[imath][/imath][imath][/imath][imath][/imath][imath][/imath]

 

[Deleted member 4993]

I always get stuck on these problems, and was wondering if anyone could explain it to me.

View attachment 33313

Since you ALWAYS get stuck and showed NO WORK, we needed to know whether you knew the basic definition.

You have NOT shown any sign of "geometric" knowledge within you.

Answer the question - politely - to receive prompt and useful help!!

 

[XxHelpMePlzxX]

Since you ALWAYS get stuck and showed NO WORK, we needed to know whether you knew the basic definition.

You have NOT shown any sign of "geometric" knowledge within you.

Answer the question - politely - to receive prompt and useful help!!

I understand where you're coming from but there is an issue I have with this. I did admit that I always get stuck on these problems, however I did ask for someone to explain this problem to me (in other words I wanted someone to walk me through this problem). That is why I didn't show any previous work. And given context such as the fact that I am going out of my way to get help on this problem, I sent a screenshot of a problem, and given the difficulty level of the problem, we can assume that I am a geometry student. This means that while I might not know how to do said problem, I am learning about geometry almost daily. Also to answer most of the questions you asked me after I posted my message, all you had to do was look at the image. For example: the congruent symbol should be obvious to anyone who takes/has taken geometry, and point E could only have been in one place. My point is instead of telling me what's wrong with what I sent, you can actually try to help me with the problem given, as I am here for math help, and not for people to critique problems that I am already struggling with.

I hope you understand.
-XxHelpMePlzxX

(P.S. Sorry for the late reply. I have been busy lately and haven't been on this site in quite some time)

 

[topsquark]

I understand where you're coming from but there is an issue I have with this. I did admit that I always get stuck on these problems, however I did ask for someone to explain this problem to me (in other words I wanted someone to walk me through this problem). That is why I didn't show any previous work. And given context such as the fact that I am going out of my way to get help on this problem, I sent a screenshot of a problem, and given the difficulty level of the problem, we can assume that I am a geometry student. This means that while I might not know how to do said problem, I am learning about geometry almost daily. Also to answer most of the questions you asked me after I posted my message, all you had to do was look at the image. For example: the congruent symbol should be obvious to anyone who takes/has taken geometry, and point E could only have been in one place. My point is instead of telling me what's wrong with what I sent, you can actually try to help me with the problem given, as I am here for math help, and not for people to critique problems that I am already struggling with.

I hope you understand.
-XxHelpMePlzxX

(P.S. Sorry for the late reply. I have been busy lately and haven't been on this site in quite some time)

The purpose of this site is to help members solve their problems. We do not, in general, simply show you the solution unless we feel it's necessary. (It does occasionally happen that showing a solution of a particular level of problem is the only way, but this is not one of those in my opinion.) However it is better if we can interactively guide you to the solution. We can't target how to help you best unless you show us where you are stuck. If you can't even start it then that's fine. You will likely be asked several leading questions to get you started. It's called the "Socratic teaching method" and is widely used.

I'm sure Subhotosh Khan knows how to solve the problem. Apparently you don't know how to start. But since you haven't given us any information about what you do already know he has to start from scratch to help you. So he asked you some basic leading questions about the diagram and problem to start you off. He does his job well and no insult was intended. This is just the way we do things here.

-Dan

Addendum: Just for the record, yes, the point E should be obvious. But clarity is important. Many diagrams posted here have had flaws and checking never hurts. Lack of a correct diagram if often a big stumbling block in getting a solution.

 

[blamocur]

I understand where you're coming from but there is an issue I have with this. I did admit that I always get stuck on these problems, however I did ask for someone to explain this problem to me (in other words I wanted someone to walk me through this problem). That is why I didn't show any previous work. And given context such as the fact that I am going out of my way to get help on this problem, I sent a screenshot of a problem, and given the difficulty level of the problem, we can assume that I am a geometry student. This means that while I might not know how to do said problem, I am learning about geometry almost daily. Also to answer most of the questions you asked me after I posted my message, all you had to do was look at the image. For example: the congruent symbol should be obvious to anyone who takes/has taken geometry, and point E could only have been in one place. My point is instead of telling me what's wrong with what I sent, you can actually try to help me with the problem given, as I am here for math help, and not for people to critique problems that I am already struggling with.

I hope you understand.
-XxHelpMePlzxX

(P.S. Sorry for the late reply. I have been busy lately and haven't been on this site in quite some time)

I see at least two posts (#4 and #8) with pointers to how to start on your problem, but I haven't seen any reaction on your part. Have you noticed them? Did you not understand them? Do you have questions about them?